Geometry & Topology

Global fixed points for centralizers and Morita's Theorem

John Franks and Michael Handel

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

mapping class group pseudo-Anosov global fixed point lifting problem


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.

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