Symmetry groups of algebraic structures and their homology

Markus Szymik, NTNU. Part of the algebra seminar series.

The symmetric groups, the general linear groups, and the automorphism groups of free groups are examples of families of groups that arise as symmetry groups of algebraic structures but that are also dear to topologists. There are many other less obvious examples of interest. For instance, in joint work with Nathalie Wahl, this point of view has led to the computation of the homology of the Higman-Thompson groups. I will survey a general context and some other geometric examples in this talk.