Global fixed points for centralizers and Morita's Theorem
Dynamical Systems
2014-11-11 v1 Geometric Topology
Abstract
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 show that there is a finite index subgroup of the centralizer of a pseudo-Anosov homeomorphism with infinitely many global fixed points. As another 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 diffeormorphisms of and we improve the lower bound for from 5 to 3.
Cite
@article{arxiv.0801.0736,
title = {Global fixed points for centralizers and Morita's Theorem},
author = {John Franks and Michael Handel},
journal= {arXiv preprint arXiv:0801.0736},
year = {2014}
}