Jacob Russell (CUNY)
Convexity in Hierarchically Hyperbolic Spaces
4:00PM, Fri Nov 30 2018, 122 Math
Convexity is a fundamental notion across a variety of flavors of geometry. In the study of the course geometry of metric spaces, it is natural to study quasiconvexity i.e. convexity with respect to quasi-geodesics. We study quasiconvexity in the class of hierarchically hyperbolic spaces; a generalization of Gromov hyperbolic spaces which contains the mapping class group, right-angled Artin and Coxeter groups, and many 3-manifold groups. Inspired by the rich theory of quasiconvexity in hyperbolic spaces, we show that quasiconvex subsets of hierarchcially hyperbolic spaces mimic the behavior of quasiconvex subsets in hyperbolic spaces.