Richard Webb (Cambridge) - How non positively curved is the mapping class group
Опубликовано: 17 Март 2026
на канале: 2017-2018 Warwick EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions
на канале: 2017-2018 Warwick EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions
491
3
Graphs, surfaces, and cube complexes
13 July 2018
Abstract: In general, mapping class groups are not CAT(0) but one is still interested in finding non-proper yet cocompact actions on CAT(0) spaces. We will show that, in general, the arc complex admits no CAT(0) metric with finitely many shapes. In particular there is no finite-index subgroup of the mapping class group that preserves a CAT(0) metric on the arc complex. The analogous statements are true for all but finitely many disc complexes of handlebodies and free splitting complexes of free groups.