Geometry & Topology

Global fixed points for centralizers and Morita's Theorem

John Franks and Michael Handel

Full-text: Open access

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.

Article information

Source
Geom. Topol., Volume 13, Number 1 (2009), 87-98.

Dates
Received: 23 April 2008
Revised: 9 September 2008
Accepted: 26 July 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800176

Digital Object Identifier
doi:10.2140/gt.2009.13.87

Mathematical Reviews number (MathSciNet)
MR2469514

Zentralblatt MATH identifier
1160.37326

Subjects
Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces 57M60: Group actions in low dimensions 37C25: Fixed points, periodic points, fixed-point index theory

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

Citation

Franks, John; Handel, Michael. Global fixed points for centralizers and Morita's Theorem. Geom. Topol. 13 (2009), no. 1, 87--98. doi:10.2140/gt.2009.13.87. https://projecteuclid.org/euclid.gt/1513800176


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