Semisimple actions of mapping class groups on CAT(0) spaces

Martin R Bridson

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arXiv · 0908.0685

Semisimple actions of mapping class groups on CAT(0) spaces

Martin R Bridson

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Abstract

Let S be an orientable surface of finite type and let Mod(S) be its mapping class group. We consider actions of Mod(S) by semisimple isometries on complete CAT(0) spaces. If the genus of S is at least 3, then in any such action all Dehn twists act as elliptic isometries. The action of Mod(S) on the completion of Teichmüller space with the Weil-Petersson metric shows that there are interesting actions of this type. Whenever the mapping class group of a closed orientable surface of genus g acts by semisimple isometries on a complete CAT(0) space of dimension less than g it must fix a point. The mapping class group of a closed surface of genus 2 acts properly by semisimple isometries on a complete CAT(0) space of dimension 18.

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BibTeX RIS

Martin R Bridson. 2009-08-05. Semisimple actions of mapping class groups on CAT(0) spaces. https://arxiv.org/abs/0908.0685

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