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Let S be an orientable surface of finite type and let Mod(S) be its mappingclass group. We consider actions of Mod(S) by semisimple isometries on completeCAT(0) spaces. If the genus of S is at least 3, then in any such action allDehn twists act as elliptic isometries. The action of Mod(S) on the completionof Teichm\"uller space with the Weil-Petersson metric shows that there areinteresting actions of this type.  Whenever the mapping class group of a closed orientable surface of genus gacts by semisimple isometries on a complete CAT(0) space of dimension less thang it must fix a point.  The mapping class group of a closed surface of genus 2 acts properly bysemisimple isometries on a complete CAT(0) space of dimension 18.

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