Volume 13, issue 1 (2009)

Download this article
For screen
For printing
Recent Issues

Volume 18 (2014)
Issue 1 1–616
Issue 2 617–1244
Issue 3 1245–1863

Volume 17 (2013) 1–5

Volume 16 (2012) 1–4

Volume 15 (2011) 1–4

Volume 14 (2010) 1–5

Volume 13 (2009) 1–5

Volume 12 (2008) 1–5

Volume 11 (2007)

Volume 10 (2006)

Volume 9 (2005)

Volume 8 (2004)

Volume 7 (2003)

Volume 6 (2002)

Volume 5 (2001)

Volume 4 (2000)

Volume 3 (1999)

Volume 2 (1998)

Volume 1 (1997)

G&T Monographs
The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

Global fixed points for centralizers and Morita's Theorem

John Franks and Michael Handel

Geometry & Topology 13 (2009) 87–98

DOI: 10.2140/gt.2009.13.87

Abstract

We prove a global fixed point theorem for the centralizer of a homeomorphism of the two-dimensional disk D that has attractor–repeller dynamics on the boundary with at least two attractors and two repellers. As one application we give an elementary proof of Morita’s Theorem, that the mapping class group of a closed surface S of genus g does not lift to the group of C2 diffeomorphisms of S and we improve the lower bound for g from 5 to 3.

Keywords

mapping class group, pseudo-Anosov, global fixed point, lifting problem

Mathematical Subject Classification

Primary: 37C25, 37E30, 57M60

Secondary:

References
Publication

Received: 23 April 2008
Revised: 9 September 2008
Accepted: 26 July 2008
Preview posted: 22 October 2008
Published: 1 January 2009
Proposed: Benson Farb
Seconded: Leonid Polterovich, Shigeyuki Morita

Authors
John Franks
Department of Mathematics
Northwestern University
Evanston, IL 60208
Michael Handel
Department of Mathematics
Lehman College
Bronx, NY 10468