Arc, disc, and sphere complexes do not admit CAT(0) metrics.

Richard Webb (Cambridge)

Wednesday 28th September, 2016 16:00-17:00 Maths 522

Abstract

A key method in geometric group theory is the analysis of groups via their action on nice spaces (e.g. CAT(0) metric spaces and complexes). In this talk we are concerned with the mapping class group and the outer automorphism group of a free group. The arc complexes, disc complexes, and free splitting/sphere complexes are contractible, Gromov hyperbolic, and every finite subgroup of their automorphism group fixes some simplex. We shall show that (almost all of) these complexes do not admit CAT(0) metrics with finitely many shapes.

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