The goal of the project is to obtain new insights into certain asymptotic topological and homological invariants of groups, specifically
- the \(\Sigma\)-invariants introduced by Bieri-Neumann-Strebel and Bieri-Renz,
- universal \(L^2\)-torsion introduced by Friedl-Lück, and
- higher generation introduced by Abels-Holz.
In the course of studying these invariants a prominent role is played by parabolic subgroups (of algebraic groups and Coxeter groups) and generalizations of these (in automorphisms of right-angles Artin groups, braid groups, etc.).