KIT | MATH | IAG | RG Topology | Topology and Geometric Group Theory | Talks - Hyperbolic groups of cohomological dimension 2

Venue:
Geb. 20.30, SR 2.058
Date:
18.07.2024
Speaker:
Rob Kropholler
Time:
15:45 Uhr
Abstract: The class of hyperbolic groups is not closed under taking subgroups or even finitely presented subgroups. This failure has lead to lots of research in geometric group theory. A positive result on subgroup closure comes from Gersten who shows that if G is hyperbolic and has integral cohomological dimension 2, then any subgroup of type FP₂(Z) is hyperbolic. Recently, this was extended to the rationals with extra hypotheses by Arora, Martinez-Pedroza and under weaker assumptions by Petrosyan, Vankov. In joint work with Bader and Vankov, we prove the same result over arbitrary, unital rings. I will discuss the background and the tools one needs to prove such results.