Cohomology, groups and negatively curved geometry

Abstract: Over the last thirty years, hyperbolic and relatively hyperbolic groups have found characterisations in terms of homological algebra in various forms, for example through bounded cohomology and bounded-valued cohomology. To link the algebra and the geometry, locally finite spaces are usually used. This can pose issues when dealing with other generalisations of hyperbolicity, such as acylindrically hyperbolic groups. To address this, in joint work with Francesco Milizia, Nansen Petrosyan and Alessandro Sisto, we study a cohomology theory that detects hyperbolicity for general metric spaces. As a consequence, we are able to provide a characterisation of hyperbolically embedded subgroups in terms of homological algebra.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.