Subgroups of word hyperbolic groups in dimension 2 over arbitrary rings

by Shaked Bader (University of Oxford)

Monday 17 Mar 2025, 14:00 → 15:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

 

In 1996 Gersten proved that if GG is a word hyperbolic group of cohomological dimension 22 and HH is a finitely presented subgroup (and actually it's enough to assume the algebraic condition FP2FP2), then H is hyperbolic as well. The definitions of cohomological dimension and FP2FP2 can be generalised for arbitrary rings. In this talk, I will present a joint work with Robert Kropholler and Vlad Vankov generalising Gersten's result to show that the same is true if GG is only assumed to have cohomological dimension 22 over some arbitrary ring RR and HH is of type FP2(R)FP2(R).