Geometry and analysis of groups and manifolds

Higher rank hyperbolicity and combinatorial dimension

speaker: Martina Joergensen

abstract: We investigate a coarse version of Dress' 2(n+1)-point inequality characterising metric spaces of combinatorial dimension at most n. This condition, experimentally referred to as (n,δ)-hyperbolicity, reduces to Gromov's quadruple definition of δ-hyperbolicity for n=1. The ℓ∞ product of n δ-hyperbolic spaces is (n,δ)-hyperbolic and, without further assumptions, any (n,δ)-hyperbolic space admits a slim (n+1)-simplex property analogous to the slimness of quasi-geodesic triangles in Gromov hyperbolic spaces. Using tools from recent advances in geometric group theory, we show that every Helly group and every hierarchically hyperbolic space of (asymptotic) rank n acts geometrically on some (n,δ)-hyperbolic space. Joint work with Urs Lang.

timetable:
Tue 27 Jun, 11:30 - 12:00, Aula Dini
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