Jump to ContentJump to Main Navigation
A Primer on Mapping Class Groups (PMS-49)$
Users without a subscription are not able to see the full content.

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, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 30 June 2022

Teichmuller Space

Teichmuller Space

(p.263) Chapter Ten Teichmüller Space
A Primer on Mapping Class Groups (PMS-49)

Benson Farb

Dan Margalit

Princeton University Press

This chapter deals with Teichmüller space Teich(S) of a surface S. It first defines Teichmüller space and a topology on Teich(S) before giving two heuristic counts of its dimension. It then describes explicit coordinates on Teich(Sɡ) coming from certain length and twist parameters for curves in a pair of pants decomposition of Sɡ; these are the Fenchel–Nielsen coordinates on Teich(Sɡ). The chapter also considers the Teichmüller space of the torus and concludes by proving the 9g – 9 theorem, which states that a hyperbolic structure on Sɡ is completely determined by the lengths assigned to 9g – 9 isotopy classes of simple closed curves in Sɡ.

Keywords:   Teichmüller space, topology, Fenchel–Nielsen coordinates, torus, hyperbolic structure, isotopy, simple closed curve

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.