The coarse Helly property, hierarchical hyperbolicity, and semihyperbolicity

Abstract: For any hierarchically hyperbolic group, and in particular any mapping class group, we define a new metric that satisfies a coarse Helly property. This enables us to deduce that the group is semihyperbolic, i.e. that it admits a bounded quasigeodesic bicombing, and also that it has finitely many conjugacy classes of finite subgroups. This has several other consequences for the group. This is a joint work with Nima Hoda and Harry Petyt.

group theorygeometric topologymetric geometry

Audience: researchers in the topic

McGill geometric group theory seminar