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arXiv · 0801.0736

Global fixed points for centralizers and Morita's Theorem

John Franks·Michael Handel
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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 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 $S$ of genus $g$ does not lift to the group of diffeormorphisms of $S$ and we improve the lower bound for $g$ from 5 to 3.

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John Franks, Michael Handel. 2008-01-04. Global fixed points for centralizers and Morita's Theorem. https://doi.org/10.2140/gt.2009.13.87

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