## Geometry & Topology

### Global fixed points for centralizers and Morita's Theorem

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

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

#### 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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