Prof. Dr. Kai-Uwe Bux
Project leader
University professor
Universität Bielefeld
E-mail: kaiuwe.bux(at)gmail.com
Telephone: +49 521 106 4988
Homepage: https://www.math.uni-bielefeld.de/~bux/
Project
39Geometric invariants of discrete and locally compact groups
8Parabolics and invariants
Publications within SPP2026
In this paper we develop the theory of homological geometric invariants (following Bieri-Neumann-Strebel-Renz) for locally compact Hausdorff groups. The homotopical version is treated elsewhere. Both versions are connected by a Hurewicz-like theorem.
Related project(s):
39Geometric invariants of discrete and locally compact groups
We extend the classical theory of homotopical Σ-sets, defined by Bieri, Neumann, Renz and Strebel for abstract groups, to locally compact Hausdorff groups. Given such a group G, our geometric invariants are sets of continuous homomorphisms G→R ("characters"). They match the classical Σ-sets if G is discrete, and refine the homotopical compactness properties of Abels and Tiemeyer. Moreover, our theory recovers the definition of low-dimensional geometric invariants for topological gropus proposed by Kochloukova.
Related project(s):
39Geometric invariants of discrete and locally compact groups
We consider the coset poset associated with the families of proper subgroups, proper subgroups of finite index, and proper normal subgroups of finite index. We investigate under which conditions those coset posets have contractiblegeometric realizations.
Related project(s):
8Parabolics and invariants