Speaker: Harsh Patil
Affiliation: University of Bristol
Title: Cohomological dimension of hyperbolic groups
Date and Time: January 29, 2025, 16:00:00 Hours
Venue: A-369
Asbtract: Hyperbolic groups are groups that act cocompactly and properly discontinuously on (Gromov)-hyperbolic metric spaces. They are a widely studied class of groups and satisfy many nice properties. We shall be interested in the cohomological dimension of these groups. To every hyperbolic group $G$ one can associate a ?space at infinity? or ?boundary?. Cohomological dimension of a group is an invariant that measures the homological complexity of its representations. The Bestvina-Mess Theorem states that the cohomological dimension of a (torsion-free) hyperbolic group is equal to the topological dimension of its boundary plus one. I will give a proof sketch of this result. Time permitting, I will discuss how this can be generalized to the class of relatively hyperbolic groups.
Affiliation: University of Bristol
Title: Cohomological dimension of hyperbolic groups
Date and Time: January 29, 2025, 16:00:00 Hours
Venue: A-369
Asbtract: Hyperbolic groups are groups that act cocompactly and properly discontinuously on (Gromov)-hyperbolic metric spaces. They are a widely studied class of groups and satisfy many nice properties. We shall be interested in the cohomological dimension of these groups. To every hyperbolic group $G$ one can associate a ?space at infinity? or ?boundary?. Cohomological dimension of a group is an invariant that measures the homological complexity of its representations. The Bestvina-Mess Theorem states that the cohomological dimension of a (torsion-free) hyperbolic group is equal to the topological dimension of its boundary plus one. I will give a proof sketch of this result. Time permitting, I will discuss how this can be generalized to the class of relatively hyperbolic groups.