Geometry and analysis of groups and manifolds

Assouad dimension and L^p-cohomology

speaker: Ursula Hamenstädt (Universität Bonn)

abstract: It is well known that a Gromov hyperbolic group admits an action on an $L^p$-space for all sufficiently large $p$ depending on the group which defines nontrivial first $L^p$-cohomology for the group. We show that the same holds true for a group which admits a non-elementary action on a Gromov hyperbolic space whose Gromov boundary has finite Assouad dimension and satisfies a strengthening of the uniformly properness condition. The hyperbolic space need not be locally compact. We give examples of groups to which this result applies, and we explain how this relates to earlier work of Bonk and Kleiner and Bourdon and Kleiner.

timetable:
Wed 28 Jun, 9:00 - 10:00, Aula Dini
<< Go back