Jump to ContentJump to Main Navigation
A Primer on Mapping Class Groups (PMS-49)$

Benson Farb and Dan Margalit

Print publication date: 2011

Print ISBN-13: 9780691147949

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691147949.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see http://www.universitypressscholarship.com/page/privacy-policy). Subscriber: null; date: 15 August 2018

(p.447) Bibliography

(p.447) Bibliography

A Primer on Mapping Class Groups (PMS-49)

Benson Farb

Dan Margalit

Princeton University Press

Bibliography references:

[1] William Abikoff. The real analytic theory of Teichm¨uller space, volume 820 of Lecture Notes in Mathematics. Springer, Berlin, 1980.

[2] Lars Ahlfors and Lipman Bers. Riemann’s mapping theorem for variable metrics. Ann. of Math. (2), 72:385–404, 1960.

[3] Lars V. Ahlfors. On quasiconformal mappings. J. Analyse Math., 3:1–58; correction, 207–208, 1954.

[4] M. A. Armstrong. The fundamental group of the orbit space of a discontinuous group. Proc. Cambridge Philos. Soc., 64:299–301, 1968.

[5] Pierre Arnoux and Jean-Christophe Yoccoz. Construction de diff´eomorphismes pseudo-Anosov. C. R. Acad. Sci. Paris S´er. I Math., 292(1):75–78, 1981.

[6] E. Artin. Theory of braids. Ann. of Math. (2), 48:101–126, 1947.

[7] M. F. Atiyah. The signature of fibre-bundles. In Global Analysis (Papers in Honor of K. Kodaira), pages 73–84. University of Tokyo Press, Tokyo, 1969.

[8] R. Baer. Kurventypen auf Fl¨achen. J. Reine Angew. Math., 156:231– 246, 1927.

[9] R. Baer. Isotopie von Kurven auf orientierbaren, geschlossenen Fl¨achen und ihr Zusammenhang mit der topologischen Deformation der Fl¨achen. J. Reine Angew. Math., 159:101–111, 1928.

[10] Walter L. Baily, Jr. On the moduli of Jacobian varieties. Ann. of Math. (2), 71:303–314, 1960.

[11] Hyman Bass and Alexander Lubotzky. Automorphisms of groups and of schemes of finite type. Israel J. Math., 44(1):1–22, 1983.

[12] Hyman Bass and Alexander Lubotzky. Linear-central filtrations on groups. In The mathematical legacy of Wilhelm Magnus: groups, (p.448) geometry and special functions (Brooklyn, NY, 1992), volume 169 of Contemp. Math., pages 45–98. American Mathematical Society, Providence, RI, 1994.

[13] Alan F. Beardon. The geometry of discrete groups, volume 91 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. Corrected reprint of the 1983 original.

[14] Lipman Bers. Quasiconformal mappings and Teichm¨uller’s theorem. In Analytic functions, pages 89–119. Princeton University Press, Princeton, NJ, 1960.

[15] Lipman Bers. An extremal problem for quasiconformal mappings and a theorem by Thurston. Acta Math., 141(1–2):73–98, 1978.

[16] Lipman Bers. An inequality for Riemann surfaces. In Differential geometry and complex analysis, pages 87–93. Springer, Berlin, 1985.

[17] M. Bestvina and M. Handel. Train-tracks for surface homeomorphisms. Topology, 34(1):109–140, 1995.

[18] Mladen Bestvina. Questions in geometric group theory. Available at http://www.math.utah.edu/~bestvina.

[19] Mladen Bestvina, Kenneth Bromberg, Koji Fujiwara, and Juan Souto. Shearing coordinates and convexity of length functions on Teichmueller space. arXiv:0902.0829, 2009.

[20] Mladen Bestvina, Kai-Uwe Bux, and Dan Margalit. Dimension of the Torelli group for Out(Fn). Invent. Math., 170(1):1–32, 2007.

[21] Joan S. Birman. Abelian quotients of the mapping class group of a 2-manifold. Bull. Amer. Math. Soc., 76:147–150, 1970.

[22] Joan S. Birman. Errata: Abelian quotients of the mapping class group of a 2-manifold. Bull. Amer. Math. Soc., 77:479, 1971.

[23] Joan S. Birman. On Siegel’s modular group. Math. Ann., 191:59–68, 1971.

[24] Joan S. Birman. Braids, links, and mapping class groups. Annals of Mathematics Studies, No. 82. Princeton University Press, Princeton, NJ, 1974.

[25] Joan S. Birman. Mapping class groups of surfaces. In Braids (Santa Cruz, CA, 1986), volume 78 of Contemporary Mathematics, pages 13–43. American Mathematical Society, Providence, RI, 1988.

(p.449) [26] Joan S. Birman and Hugh M. Hilden. On the mapping class groups of closed surfaces as covering spaces. In Advances in the theory of Riemann surfaces (Stony Brook, N. Y., 1969), Annals of Mathematics Studies, No. 66, pages 81–115. Princeton University Press, Princeton, NJ, 1971.

[27] Joan S. Birman and Hugh M. Hilden. On isotopies of homeomorphisms of Riemann surfaces. Ann. of Math. (2), 97:424–439, 1973.

[28] Joan S. Birman, Alex Lubotzky, and John McCarthy. Abelian and solvable subgroups of the mapping class groups. Duke Math. J., 50(4):1107–1120, 1983.

[29] Joan S. Birman and Bronislaw Wajnryb. Presentations of the mapping class group. Errata: “3-fold branched coverings and the mapping class group of a surface” [Geometry and topology (College Park, MD, 1983/1984), 24–46, Lecture Notes in Mathematics, 1167, Springer, Berlin, 1985] and “A simple presentation of the mapping class group of an orientable surface” [Israel J. Math. 45 2–3, 157–174, 1983]. Israel J. Math., 88(1–3):425–427, 1994.

[30] Søren Kjærgaard Boldsen. Different versions of mapping class groups of surfaces. arXiv:0908.2221, 2009.

[31] Francis Bonahon. The geometry of Teichm¨uller space via geodesic currents. Invent. Math., 92(1):139–162, 1988.

[32] Tara E. Brendle and Benson Farb. Every mapping class group is generated by 6 involutions. J. Algebra, 278(1):187–198, 2004.

[33] Tara E. Brendle and Dan Margalit. Commensurations of the Johnson kernel. Geom. Topol., 8:1361–1384, 2004 (electronic).

[34] Tara E. Brendle and Dan Margalit. Addendum to: “Commensurations of the Johnson kernel” (Geom. Topol. 8: (2004); 1361–1384, MR2119299). Geom. Topol., 12(1):97–101, 2008.

[35] Martin R. Bridson and Andr´e Haefliger. Metric spaces of non-positive curvature, volume 319 of Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences). Springer-Verlag, Berlin, 1999.

[36] L. E. J. Brouwer. Beweis der invarianz des n-dimensionalen gebiets. Math. Ann., 71(3):305–313, 1911.

(p.450) [37] Kenneth S. Brown. Presentations for groups acting on simply-connected complexes. J. Pure Appl. Algebra, 32(1):1–10, 1984.

[38] Kenneth S. Brown. Cohomology of groups, volume 87 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1994. Corrected reprint of the 1982 original.

[39] Ronald Brown and Philip J. Higgins. The fundamental groupoid of the quotient of a Hausdorff space by a discontinuous action of a discrete group is the orbit groupoid of the induced action. University of Wales, Bangor, Maths Preprint 02.25.

[40] Heinrich Burkhardt. Grundz¨uge einer allgemeinen Systematik der hyperelliptischen Functionen I. Ordnung. Mathematische Annalen, 35:198–296, 1890.

[41] W. Burnside. Theory of groups of finite order, 2nd ed. Dover Publications, New York, 1955.

[42] Peter Buser. Geometry and spectra of compact Riemann surfaces, volume 106 of Progress in Mathematics. Birkh¨auser, Boston, MA, 1992.

[43] Danny Calegari. Foliations and the geometry of 3-manifolds. Oxford Mathematical Monographs. Oxford University Press, Oxford, 2007.

[44] Andrew J. Casson and Steven A. Bleiler. Automorphisms of surfaces after Nielsen and Thurston, volume 9 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 1988.

[45] Jean Cerf. Topologie de certains espaces de plongements. Bull. Soc. Math. France, 89:227–380, 1961.

[46] D. R. J. Chillingworth. Winding numbers on surfaces. II. Math. Ann., 199:131–153, 1972.

[47] Thomas Church and Benson Farb. Parametrized Abel-Jacobi maps, a question of Johnson, and a homological stability conjecture for the Torelli group. arXiv:1001.1114, 2010.

[48] John B. Conway. Functions of one complex variable, 2nd ed, volume 11 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1978.

[49] M. Dehn. Lecture notes from the Breslau Mathematics Colloquium. Archives of the University of Texas at Austin, 1922.

(p.451) [50] M. Dehn. Die Gruppe der Abbildungsklassen. Acta Math., 69(1):135–206, 1938. Das arithmetische Feld auf Fl¨achen.

[51] Max Dehn. Papers on group theory and topology. Springer-Verlag, New York, 1987. Translated from the German and with introductions.

[52] P. Deligne and D. Mumford. The irreducibility of the space of curves of given genus. Inst. Hautes E´tudes Sci. Publ. Math., (36):75–109, 1969.

[53] Clifford J. Earle and James Eells. A fibre bundle description of Teichm¨uller theory. J. Differential Geometry, 3:19–43, 1969.

[54] James Eells, Jr. and J. H. Sampson. Harmonic mappings of Riemannian manifolds. Amer. J. Math., 86:109–160, 1964.

[55] V.A. Efremoviˇc. On the proximity geometry of Riemannian manifolds. Uspekhi Math Nauk, 8:189, 1953.

[56] D. B. A. Epstein. Curves on 2-manifolds and isotopies. Acta Math., 115:83–107, 1966.

[57] Edward Fadell and Lee Neuwirth. Configuration spaces. Math. Scand., 10:111–118, 1962.

[58] Benson Farb, editor. Problems on mapping class groups and related topics, volume 74 of Proceedings of Symposia in Pure Mathematics. American Mathematical Society, Providence, RI, 2006.

[59] Benson Farb and Nikolai V. Ivanov. The Torelli geometry and its applications: research announcement. Math. Res. Lett., 12(2-3):293– 301, 2005.

[60] H. M. Farkas and 2nd ed Kra, I. Riemann surfaces, volume 71 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1992.

[61] A. Fathi, F. Laudenbach, and V. Po´enaru, editors. Travaux de Thurston sur les surfaces, volume 66 of Ast´erisque. Soci´et´e Math´ematique de France, Paris, 1979. S´eminaire Orsay, with an English summary.

[62] W. Fenchel. Estensioni di gruppi discontinui e trasformazioni periodiche delle superficie. Atti Accad. Naz Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8), 5:326–329, 1948.

(p.452) [63] W. Fenchel. Remarks on finite groups of mapping classes. Mat. Tidsskr. B., 1950:90–95, 1950.

[64] Werner Fenchel and Jakob Nielsen. Discontinuous groups of isometries in the hyperbolic plane, volume 29 of de Gruyter Studies in Mathematics. Walter de Gruyter, Berlin, 2003. Edited and with a preface by Asmus L. Schmidt, and a biography of the authors by Bent Fuglede.

[65] Ralph H. Fox. Free differential calculus. I. Derivation in the free group ring. Ann. of Math. (2), 57:547–560, 1953.

[66] J. Franks and E. Rykken. Pseudo-Anosov homeomorphisms with quadratic expansion. Proc. Amer. Math. Soc., 127(7):2183–2192, 1999.

[67] Robert Fricke and Felix Klein. Vorlesungen ¨uber die Theorie der automorphen Funktionen. Band 1: Die gruppentheoretischen Grundlagen. Band II: Die funktionentheoretischen Ausf¨uhrungen und die Andwendungen, volume 4 of Bibliotheca Mathematica Teubneriana, B¨ande 3. Johnson Reprint, New York, 1965.

[68] William Fulton. Algebraic curves. Advanced Book Classics. Addison-Wesley, Redwood City, CA, 1989. An introduction to algebraic geometry, with notes written with the collaboration of Richard Weiss. Reprint of 1969 original.

[69] F. R. Gantmacher. The theory of matrices. Vols. 1 and 2. Translated by K. A. Hirsch. Chelsea Publishing, New York, 1959.

[70] Frederick P. Gardiner and Nikola Lakic. Quasiconformal Teichm¨uller theory, volume 76 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2000.

[71] Sylvain Gervais. Presentation and central extensions of mapping class groups. Trans. Amer. Math. Soc., 348(8):3097–3132, 1996.

[72] Jane Gilman. On the Nielsen type and the classification for the mapping class group. Adv. Math., 40(1):68–96, 1981.

[73] Andr´e Gramain. Le type d’homotopie du groupe des diff´eomorphismes d’une surface compacte. Ann. Sci. E´cole Norm. Sup. (4), 6:53–66, 1973.

[74] Edna K. Grossman. On the residual finiteness of certain mapping class groups. J. London Math. Soc. (2), 9:160–164, 1974/75.

(p.453) [75] Ursula Hamenst¨adt. Length functions and parameterizations of Teichm¨uller space for surfaces with cusps. Ann. Acad. Sci. Fenn. Math., 28(1):75–88, 2003.

[76] Hessam Hamidi-Tehrani. Groups generated by positive multi-twists and the fake lantern problem. Algebr. Geom. Topol., 2:1155–1178, 2002 (electronic).

[77] Mary-Elizabeth Hamstrom. Some global properties of the space of homeomorphisms on a disc with holes. Duke Math. J., 29:657–662, 1962.

[78] Mary-Elizabeth Hamstrom. The space of homeomorphisms on a torus. Illinois J. Math., 9:59–65, 1965.

[79] Mary-Elizabeth Hamstrom. Homotopy groups of the space of homeomorphisms on a 2-manifold. Illinois J. Math., 10:563–573, 1966.

[80] Michael Handel. Global shadowing of pseudo-Anosov homeomorphisms. Ergodic Theory Dynam. Systems, 5(3):373–377, 1985.

[81] Michael Handel and William P. Thurston. New proofs of some results of Nielsen. Adv. in Math., 56(2):173–191, 1985.

[82] John Harer. The fourth homology group of the moduli space of curves. Unpublished.

[83] John Harer. The second homology group of the mapping class group of an orientable surface. Invent. Math., 72(2):221–239, 1983.

[84] John Harer. The cohomology of the moduli space of curves. In Theory of moduli (Montecatini Terme, 1985), volume 1337 of Lecture Notes in Mathematics, pages 138–221. Springer, Berlin, 1988.

[85] John Harer. The third homology group of the moduli space of curves. Duke Math. J., 63(1):25–55, 1991.

[86] John L. Harer. Stability of the homology of the mapping class groups of orientable surfaces. Ann. of Math. (2), 121(2):215–249, 1985.

[87] John L. Harer. The virtual cohomological dimension of the mapping class group of an orientable surface. Invent. Math., 84(1):157–176, 1986.

(p.454) [88] W. J. Harvey. Boundary structure of the modular group. In Riemann surfaces and related topics: (Stony Brook, NY, 1978), volume 97 of Annals of Mathematics Studies, pages 245–251, Princeton, NJ, 1981. Princeton University Press.

[89] A. Hatcher and W. Thurston. A presentation for the mapping class group of a closed orientable surface. Topology, 19(3):221–237, 1980.

[90] Allen Hatcher. On triangulations of surfaces. Topology Appl., 40(2):189–194, 1991.

[91] Allen Hatcher. Algebraic topology. Cambridge University Press, Cambridge, 2002.

[92] Allen Hatcher, Pierre Lochak, and Leila Schneps. On the Teichm¨uller tower of mapping class groups. J. Reine Angew. Math., 521:1–24, 2000.

[93] John Hempel. 3-manifolds. AMS Chelsea Publishing, Providence, RI, 2004. Reprint of the 1976 original.

[94] Susumu Hirose. A complex of curves and a presentation for the mapping class group of a surface. Osaka J. Math., 39(4):795–820, 2002.

[95] Morris W. Hirsch. Differential topology, volume 33 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1994. Corrected reprint of the 1976 original.

[96] John Hubbard and Howard Masur. Quadratic differentials and foliations. Acta Math., 142(3-4):221–274, 1979.

[97] John Hamal Hubbard. Teichm¨uller theory and applications to geometry, topology, and dynamics. Vol. 1. Matrix Editions, Ithaca, NY, 2006. Teichm¨uller theory, with contributions by Adrien Douady, William Dunbar, Roland Roeder, Sylvain Bonnot, David Brown, Allen Hatcher, Chris Hruska, and Sudeb Mitra, and with forewords by William Thurston and Clifford Earle.

[98] Heinz Huber. Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen. Math. Ann., 138:1–26, 1959.

[99] Heinz Huber. Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II. Math. Ann., 142:385–398, 1960/1961.

[100] Heinz Huber. Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II. Math. Ann., 143:463–464, 1961.

(p.455) [101] Stephen P. Humphries. Generators for the mapping class group. In Topology of low-dimensional manifolds (Chelwood Gate, 1977), volume 722 of Lecture Notes in Mathematics, pages 44–47. Springer, Berlin, 1979.

[102] A. Hurwitz. Ueber Riemann’sche Fl¨achen mit gegebenen Verzweigungspunkten. Math. Ann., 39(1):1–60, 1891.

[103] Atsushi Ishida. The structure of subgroup of mapping class groups generated by two Dehn twists. Proc. Japan Acad. Ser. A Math. Sci., 72(10):240–241, 1996.

[104] N. V. Ivanov. Coefficients of expansion of pseudo-Anosov homeomorphisms. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 167(Issled. Topol. 6):111–116, 191, 1988.

[105] N. V. Ivanov. Residual finiteness of modular Teichm¨uller groups. Sibirsk. Mat. Zh., 32(1):182–185, 222, 1991.

[106] Nikolai V. Ivanov. Subgroups of Teichm¨uller modular groups, volume 115 of Translations of Mathematical Monographs. American Mathematical Society, Providence, RI, 1992. Translated from the Russian by E. J. F. Primrose and revised by the author.

[107] Nikolai V. Ivanov. Mapping class groups. In Handbook of geometric topology, pages 523–633. North-Holland, Amsterdam, 2002.

[108] Nikolai V. Ivanov and Lizhen Ji. Infinite topology of curve complexes and non-Poincar´e duality of Teichmueller modular groups. arXiv:0707.4322v1, 2007.

[109] Dennis Johnson. An abelian quotient of the mapping class group Ig. Math. Ann., 249(3):225–242, 1980.

[110] Dennis Johnson. Conjugacy relations in subgroups of the mapping class group and a group-theoretic description of the Rochlin invariant. Math. Ann., 249(3):243–263, 1980.

[111] Dennis Johnson. The structure of the Torelli group. I. A finite set of generators for I. Ann. of Math. (2), 118(3):423–442, 1983.

[112] Dennis Johnson. A survey of the Torelli group. In Low-dimensional topology (San Francisco, CA, 1981), volume 20 of Contemporary Mathematics, pages 165–179. AmericanMathematical Society, Providence, RI, 1983.

(p.456) [113] Dennis Johnson. The structure of the Torelli group. II. A characterization of the group generated by twists on bounding curves. Topology, 24(2):113–126, 1985.

[114] Dennis Johnson. The structure of the Torelli group. III. The abelianization of T . Topology, 24(2):127–144, 1985.

[115] Dennis L. Johnson. Homeomorphisms of a surface which act trivially on homology. Proc. Amer. Math. Soc., 75(1):119–125, 1979.

[116] Michael Kapovich. Hyperbolic manifolds and discrete groups, volume 183 of Progress inMathematics. Birkh¨auser, Boston, MA, 2001.

[117] Martin Kassabov. Generating mapping class groups by involutions. math.GT/0311455, 2003.

[118] Christian Kassel and Vladimir Turaev. Braid groups, volume 247 of Graduate Texts in Mathematics. Springer, New York, 2008. With the graphical assistance of Olivier Dodane.

[119] Svetlana Katok. Fuchsian groups. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1992.

[120] Linda Keen. Collars on Riemann surfaces. In Discontinuous groups and Riemann surfaces (College Park, MD., 1973), pages 263– 268. Annals of Mathematics Studies, No. 79. Princeton Univ. Press, Princeton, NJ, 1974.

[121] Richard P. Kent, IV, Christopher J. Leininger, and Saul Schleimer. Trees and mapping class groups. J. Reine Angew. Math., 637:1–21, 2009.

[122] Steven P. Kerckhoff. The Nielsen realization problem. Ann. of Math. (2), 117(2):235–265, 1983.

[123] Rob Kirby. Problems in low-dimensional topology. Available at http://math.berkeley.edu/~kirby.

[124] Mustafa Korkmaz. Low-dimensional homology groups of mapping class groups: a survey. Turkish J. Math., 26(1):101–114, 2002.

[125] Mustafa Korkmaz. Generating the surface mapping class group by two elements. Trans. Amer. Math. Soc., 357(8):3299–3310, 2005 (electronic).

(p.457) [126] Mustafa Korkmaz and Andr´as I. Stipsicz. The second homology groups of mapping class groups of oriented surfaces. Math. Proc. Cambridge Philos. Soc., 134(3):479–489, 2003.

[127] Irwin Kra. On the Nielsen–Thurston–Bers type of some self-maps of Riemann surfaces. Acta Math., 146(3–4):231–270, 1981.

[128] Ravi S. Kulkarni. Riemann surfaces admitting large automorphism groups. In Extremal Riemann surfaces (San Francisco, CA, 1995), volume 201 of Contemporary Mathematics, pages 63–79. American Mathematical Society, Providence, RI, 1997.

[129] Michael Larsen. How often is 84(g − 1) achieved? Israel J. Math., 126:1–16, 2001.

[130] M. A. Lavrentiev. Sur une classe des repr´esentations continues. Mat. Sb., 42:407–434, 1935.

[131] W. B. R. Lickorish. A finite set of generators for the homeotopy group of a 2-manifold. Proc. Cambridge Philos. Soc., 60:769–778, 1964.

[132] Feng Luo. Torsion Elements in the Mapping Class Group of a Surface.

[133] Roger C. Lyndon and Paul E. Schupp. Combinatorial group theory. Classics in Mathematics. Springer-Verlag, Berlin, 2001. Reprint of the 1977 edition.

[134] A. M. Macbeath. On a theorem by J. Nielsen. Quart. J. Math. Oxford Ser. (2), 13:235–236, 1962.

[135] Colin Maclachlan. Modulus space is simply-connected. Proc. Amer. Math. Soc., 29:85–86, 1971.

[136] Wilhelm Magnus. Untersuchungen ¨uber einige unendliche diskontinuierliche Gruppen. Math. Ann., 105(1):52–74, 1931.

[137] Wilhelm Magnus. Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring. Math. Ann., 111(1):259–280, 1935.

[138] Wilhelm Magnus, Abraham Karrass, and Donald Solitar. Combinatorial group theory, 2nd ed. Dover Publications Inc., Mineola, NY, 2004. Presentations of groups in terms of generators and relations.

(p.458) [139] K. Mahler. On lattice points in n-dimensional star bodies. I. Existence theorems. Proc. Roy. Soc. London. Ser. A., 187:151–187, 1946.

[140] Albert Marden and Kurt Strebel. A characterization of Teichm¨uller differentials. J. Differential Geom., 37(1):1–29, 1993.

[141] Dan Margalit and Jon McCammond. Geometric presentations for the pure braid group. J. Knot Theory Ramifications, 18(1):1–20, 2009.

[142] J. Peter Matelski. A compactness theorem for Fuchsian groups of the second kind. Duke Math. J., 43(4):829–840, 1976.

[143] Makoto Matsumoto. A simple presentation of mapping class groups in terms of Artin groups [translation of S¯ugaku 52, no. 1, 31–42, 2000; 1764273]. Sugaku Expositions, 15(2):223–236, 2002. Sugaku expositions.

[144] John D. McCarthy. Automorphisms of surface mapping class groups. A recent theorem of N. Ivanov. Invent. Math., 84(1):49–71, 1986.

[145] James McCool. Some finitely presented subgroups of the automorphism group of a free group. J. Algebra, 35:205–213, 1975.

[146] Darryl McCullough and Andy Miller. The genus 2 Torelli group is not finitely generated. Topology Appl., 22(1):43–49, 1986.

[147] Darryl McCullough and Kashyap Rajeevsarathy. Roots of Dehn twists. arXiv:0906.1601v1, 2009.

[148] Dusa McDuff and Dietmar Salamon. Introduction to symplectic topology, 2nd ed. Oxford Mathematical Monographs. Clarendon Press Oxford University Press, New York, 1998.

[149] H. P. McKean. Selberg’s trace formula as applied to a compact Riemann surface. Comm. Pure Appl. Math., 25:225–246, 1972.

[150] H. P. McKean. Correction to: “Selberg’s trace formula as applied to a compact Riemann surface” (Comm. Pure Appl. Math. 25: 225–246, 1972). Comm. Pure Appl. Math., 27:134, 1974.

[151] Curtis T. McMullen. Polynomial invariants for fibered 3-manifolds and Teichm¨uller geodesics for foliations. Ann. Sci. E´cole Norm. Sup. (4), 33(4):519–560, 2000.

[152] Curtis T. McMullen. Personal communication. 2010.

(p.459) [153] William H. Meeks, III and Julie Patrusky. Representing homology classes by embedded circles on a compact surface. Illinois J. Math., 22(2):262–269, 1978.

[154] J.Mennicke. Zur Theorie der Siegelschen Modulgruppe. Math. Ann., 159:115–129, 1965.

[155] Geoffrey Mess. The Torelli groups for genus 2 and 3 surfaces. Topology, 31(4):775–790, 1992.

[156] Werner Meyer. Die Signatur von Fl¨achenb¨undeln. Math. Ann., 201:239–264, 1973.

[157] Richard T. Miller. Geodesic laminations from Nielsen’s viewpoint. Adv. in Math., 45(2):189–212, 1982.

[158] J. Milnor. A note on curvature and fundamental group. J. Differential Geometry, 2:1–7, 1968.

[159] John Milnor. Construction of universal bundles. II. Ann. of Math. (2), 63:430–436, 1956.

[160] Shigeyuki Morita. Characteristic classes of surface bundles. Invent. Math., 90(3):551–577, 1987.

[161] Shigeyuki Morita. Casson’s invariant for homology 3-spheres and characteristic classes of surface bundles. I. Topology, 28(3):305–323, 1989.

[162] Charles B. Morrey, Jr. On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer.Math. Soc., 43(1):126–166, 1938.

[163] Lee Mosher. Mapping class groups and Out(Fr). Available at http://aimath.org/pggt.

[164] David Mumford. Abelian quotients of the Teichm¨uller modular group. J. Analyse Math., 18:227–244, 1967.

[165] David Mumford. Abelian quotients of the Teichm¨uller modular group. J. Analyse Math., 18:227–244, 1967.

[166] David Mumford. A remark on Mahler’s compactness theorem. Proc. Amer. Math. Soc., 28:289–294, 1971.

[167] James Munkres. Obstructions to the smoothing of piecewise-differentiable homeomorphisms. Ann. of Math. (2), 72:521–554, 1960.

(p.460) [168] Jakob Nielsen. Untersuchungen zur Topologie der geschlossenen zweseitigen Fl¨achen. Acta Math., 50:189–358, 1927.

[169] Jakob Nielsen. Untersuchungen zur Topologie der geschlossenen zweiseitigen Fl¨achen. II. Acta Math., 53(1):1–76, 1929.

[170] Jakob Nielsen. Untersuchungen zur Topologie der geschlossenen zweiseitigen Fl¨achen. III. Acta Math., 58(1):87–167, 1932.

[171] Jakob Nielsen. Abbildungsklassen endlicher Ordnung. Acta Math., 75:23–115, 1943.

[172] Jakob Nielsen. Surface transformation classes of algebraically finite type. Danske Vid. Selsk. Math.-Phys. Medd., 21(2):89, 1944.

[173] Jean-Pierre Otal. Le th´eor`eme d’hyperbolisation pour les vari´et´es fibr´ees de dimension 3. Ast´erisque, (235):x+159, 1996.

[174] Luis Paris. Personal communication. 2010.

[175] R. C. Penner. Bounds on least dilatations. Proc. Amer. Math. Soc., 113(2):443–450, 1991.

[176] R. C. Penner and J. L. Harer. Combinatorics of train tracks, volume 125 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 1992.

[177] Robert C. Penner. A construction of pseudo-Anosov homeomorphisms. Trans. Amer. Math. Soc., 310(1):179–197, 1988.

[178] Bernard Perron and Jean-Pierre Vannier. Groupe de monodromie g´eom´etrique des singularit´es simples. C. R. Acad. Sci. Paris S´er. I Math., 315(10):1067–1070, 1992.

[179] Wolfgang Pitsch. Un calcul ´el´ementaire de H2(Mg,1,Z) pour g ≥ 4. C. R. Acad. Sci. Paris S´er. I Math., 329(8):667–670, 1999.

[180] Jerome Powell. Two theorems on the mapping class group of a surface. Proc. Amer. Math. Soc., 68(3):347–350, 1978.

[181] Jerome Powell. Homeomorphisms of S3 leaving a Heegaard surface invariant. Trans. Amer. Math. Soc., 257(1):193–216, 1980.

[182] J´ozef H. Przytycki. History of the knot theory from Vandermonde to Jones. In XXIVth National Congress of the Mexican Mathematical Society (Spanish) (Oaxtepec, 1991), volume 11 of Aportaciones Matem´aticas Comunicaciones, pages 173–185. Sociedad Matem´aticas Mexicana, M´exico, 1992.

(p.461) [183] Andrew Putman. Abelian covers of surfaces and the homology of the level l mapping class group. arXiv:0907.1718v2, 2009.

[184] Andrew Putman. Cutting and pasting in the Torelli group. Geom. Topol., 11:829–865, 2007.

[185] Bernhard Riemann. Theorie der abelschen functionen. J. Reine Angew. Math., Band 54, 1857.

[186] H. L. Royden. Automorphisms and isometries of Teichm¨uller space. In Advances in the Theory of Riemann Surfaces (Stony Brook, NY, 1969), pages 369–383. Annals of Mathematics Studies, No. 66. Princeton University Press, Princeton, NJ, 1971.

[187] Walter Rudin. Real and complex analysis. McGraw-Hill, New York, 1966.

[188] Hermann Ludwig Schmid and Oswald Teichm¨uller. Ein neuer Beweis f ¨ur die Funktionalgleichung der L-Reihen. Abh. Math. Sem. Hansischen Univ., 15:85–96, 1943.

[189] Richard Schoen and Shing Tung Yau. On univalent harmonic maps between surfaces. Invent. Math., 44(3):265–278, 1978.

[190] Peter Scott. The geometries of 3-manifolds. Bull. London Math. Soc., 15(5):401–487, 1983.

[191] Peter Scott and Terry Wall. Topological methods in group theory. In Homological group theory (Durham, 1977), volume 36 of London Mathematical Society Lecture Note Series, pages 137–203. Cambridge University Press, Cambridge, 1979.

[192] Herbert Seifert. Bemerkungen zur stetigen abbildung von fl¨achen. Abh. Math. Sem. Univ. Hamburg, 12:23–37, 1937.

[193] Atle Selberg. On discontinuous groups in higher-dimensional symmetric spaces. In Contributions to function theory (International Colloquium on Function Theory, Bombay, 1960), pages 147–164. Tata Institute of Fundamental Research, Bombay, 1960.

[194] J.-P. Serre. Rigidit´e de foncteur d’Jacobi d’´echelon n ≥ 3. Sem. H. Cartan, 1960/1961, appendix to Exp. 17, 1961.

[195] Jean-Pierre Serre. Trees. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2003. Translated from the French original by John Stillwell, corrected second printing of the 1980 English translation.

(p.462) [196] Ya. G. Sinai. Introduction to ergodic theory. Mathematical Notes, No. 18. Princeton University Press, Princeton, NJ, 1976. Translated by V. Scheffer.

[197] Stephen Smale. Diffeomorphisms of the 2-sphere. Proc. Amer. Math. Soc., 10:621–626, 1959.

[198] George Springer. Introduction to Riemann surfaces. Addison-Wesley, Reading, MA, 1957.

[199] John C. Stillwell. Classical topology and combinatorial group theory, volume 72 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1980.

[200] Kurt Strebel. Quadratic differentials, volume 5 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]. Springer-Verlag, Berlin, 1984.

[201] Toshikazu Sunada. Riemannian coverings and isospectral manifolds. Ann. of Math. (2), 121(1):169–186, 1985.

[202] A. S. Sˇvarc. A volume invariant of coverings. Dokl. Akad. Nauk SSSR (N.S.), 105:32–34, 1955.

[203] Oswald Teichm¨uller. Extremale quasikonforme Abbildungen und quadratische Differentiale. Abh. Preuss. Akad. Wiss. Math.-Nat. Kl., 1939(22):197, 1940.

[204] Carsten Thomassen. The Jordan–Sch¨onflies theorem and the classification of surfaces. Amer. Math. Monthly, 99(2):116–130, 1992.

[205] W. P. Thurston. Hyperbolic structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle. arXiv:math.GT/9801045, 1986.

[206] William P. Thurston. The geometry and topology of 3-manifolds. Princeton University Notes, Princeton University, Princeton, NJ, 1980.

[207] William P. Thurston. On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Amer. Math. Soc. (N.S.), 19(2):417–431, 1988.

[208] William P. Thurston. Three-dimensional geometry and topology. Vol. 1, volume 35 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 1997. Edited by Silvio Levy.

(p.463) [209] Bronislaw Wajnryb. A simple presentation for the mapping class group of an orientable surface. Israel J. Math., 45(2-3):157–174, 1983.

[210] Bronislaw Wajnryb. An elementary approach to the mapping class group of a surface. Geom. Topol., 3:405–466, 1999 (electronic).

[211] B. A. F. Wehrfritz. Infinite linear groups. An account of the group-theoretic properties of infinite groups of matrices. Springer-Verlag, New York, 1973. Ergebnisse der Matematik und ihrer Grenzgebiete, Band 76.

[212] Andr´e Weil. On discrete subgroups of Lie groups. Ann. of Math. (2), 72:369–384, 1960.

[213] J. H. C. Whitehead. Manifolds with transverse fields in euclidean space. Ann. of Math. (2), 73:154–212, 1961.

[214] A. Wiman. Uber die hyperelliptischen Curven und diejenigan vom Geschlechte p = 3, welche eindeutigen Transformationen in sich zulassen. Bihang Kongl. Svenska Vetenskaps-Akademiens Handlingar, 1895-1896.

[215] Scott Wolpert. The length spectra as moduli for compact Riemann surfaces. Ann. of Math. (2), 109(2):323–351, 1979.

[216] Scott A. Wolpert. Families of Riemann surfaces and Weil-Petersson geometry, volume 113 of CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC, 2010.

[217] Tatsuhiko Yagasaki. Homotopy types of homeomorphism groups of noncompact 2-manifolds. Topology Appl., 108(2):123–136, 2000.

[218] Heiner Zieschang, Elmar Vogt, and Hans-Dieter Coldewey. Surfaces and planar discontinuous groups, volume 835 of Lecture Notes in Mathematics. Springer, Berlin, 1980. Translated from the German by John Stillwell.