Research Group Geometry, Topology and Group Theory

Bielefeld-Münster Seminar on

Groups, Geometry and Topology

Friday, January 24, 2025.

All lectures take place in room SRZ 214, Orleans-Ring 12, 48149 in Münster.

Talks:

10:15 Sam Shepard (Münster) Product separability for special cube complexes

Abstract: I will talk about my new result regarding the separability of products of subgroups for groups that admit a virtually special action on a CAT(0) cube complex. My talk will also contain lots of background on cube complexes and virtual specialness, which has been an important topic in geometric group theory over the last 20 years, particularly with the connection to 3-manifold theory.

11:15: Coffee break

11:45 Sebastian Degen (Bielefeld) Most q-matroids are not representable

Abstract: The q-analogue of a combinatorial object arises by replacing finite sets with finite dimensional vector spaces. In particular we can view q-matroids as q-analogues of matroids. One motivation to study q-matroids stems from coding theory, as the representable q-matroids arise from rank-metric codes. In the matroidal setting Peter Nelson proved in 2018 that asymptotically almost all matroids are non-representable, therefore one can ask if the same holds true in the q-analogue. In this talk we investigate this question and provide a positive answer to it. For this purpose we give a lower bound on the number of all fixed dimensional q-matroids, using the theory of constant dimension codes and an upper bound on the number of all representable q-matroids, using the concept of zero patterns.

12:45 Lunch break

14:00 Philip Möller (Düsseldorf) Profinite rigidity and the isomorphism problem for Coxeter groups

Abstract: A finitely generated residually finite group G is called profinitely rigid if it is determined up to isomorphism by its finite quotients amongst all finitely generated residually finite groups. In this talk I will discuss recent progress on this question in the context of Coxeter groups. Moreover, I will explain the connection of this problem to the isomorphism problem of Coxeter groups. This is joint work with Sam Corson, Sam Hughes and Olga Varghese.

15:00 Coffee break

15:30 Elisa Hartmann (Bielefeld) Geometric invariants of locally compact groups, homological version

Abstract: In this talk we present the homological version of Σ-theory for locally compact Hausdorff groups, the corresponding talk for the homotopical version has been given by José last year in the same seminar. Both versions are connected by a Hurewicz-like theorem. They can be thought of as directional versions of type CP_m and type C_m, respectively. And classical Σ-theory is recovered if we equip an abstract group with the discrete topology.
We provide criteria for type CP_m and homological locally compact Σ^m. In the setting of an exact sequence of locally compact Hausdorff groups, we study in which way compactness properties of the kernel/extension/quotient can be derived from the other two groups in the sequence. This project is joint work with Kai-Uwe Bux and José Pedro Quintanilha.

Organizers: Barbara Baumeister, Kai-Uwe Bux and Linus Kramer.

Supported by Mathematics Münster and TRR 358 Integral Structures and Representation Theory.