Geometry & Topology
- Geom. Topol.
- Volume 13, Number 1 (2009), 87-98.
Global fixed points for centralizers and Morita's Theorem
We prove a global fixed point theorem for the centralizer of a homeomorphism of the two-dimensional disk 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 of genus does not lift to the group of diffeomorphisms of and we improve the lower bound for from to .
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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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