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Frontiers in Complex DynamicsIn Celebration of John Milnor's 80th Birthday$
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Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Print publication date: 2014

Print ISBN-13: 9780691159294

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159294.001.0001

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Two papers which changed my life: Mil nor's seminal work on flat manifolds and bundles

Two papers which changed my life: Mil nor's seminal work on flat manifolds and bundles

Chapter:
(p.679) Two papers which changed my life: Milnor's seminal work on flat manifolds and bundles
Source:
Frontiers in Complex Dynamics
Author(s):
Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159294.003.0024

This chapter surveys developments arising from John Milnor's 1958 paper, “On the existence of a connection with curvature zero” and his 1977 paper, “On fundamental groups of complete affinely flat manifolds.” The former deeply influenced the theory of characteristic classes of flat bundles, and the latter clarified the theory of affine manifolds, setting the stage for its future flourishing. This chapter begins with some reminiscences on Milnor. It then describes the history of the Milnor–Wood inequality and the Auslander Conjecture and then proceeds to more recent developments, including a description of Margulis space-times, a startling example of an affine three-manifold with free fundamental group.

Keywords:   John Milnor, flat manifolds, flat bundles, affine manifolds, Milnor–Wood inequality, Auslander Conjecture, Margulis space-times

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