Arbeitsgruppe Geometrie, Topologie und Gruppentheorie

Bielefeld-Münster Seminar on

Groups, Geometry and Topology

Wednesday, February 8, 2023.

All lectures take place in room SRZ 216/217, Orleans-Ring 12, 48149 Münster.

Talks:

10:00 Daniel Keppeler (Münster) Automatic continuity for graph products

Abstract: The automatic continuity problem asks the following question: Given two topological groups G and H and an algebraic homomorphism f between those, what are conditions on the groups G and H, such that f is automatically continuous? In this talk, we will give an introduction to this problem, where G is topologically rich (e.g. locally compact or Čech complete) and H is a discrete geometric group and in particular a graph product of groups.

11:00 Coffee break

11:30 Amandine Escalier (Münster) An overview on Local-to-Global rigidity

Abstract: We say that a graph G is Local-to-Global rigid if there exists R>0 such that every other graph whose balls of radius R are isometric to the balls of radius R in G is covered by G. In this talk we provide an overview of this rigidity notion, using buildings as a background scene. We’ll talk about the motivations, discuss numerous examples and borrow topological tools to settle the basis. In a second part, we will see the known cases where LG-rigidity is invariant under quasi-isometry and discuss some strategies to prove this invariance.
You can download the slides and written notes.

12:30 Lunch break

14:00 Jonas Flechsig (Bielefeld) Orbifold mapping class groups and orbifold braid groups

Abstract: A useful approach to study Artin's braid group B_n is its identification with the mapping class group Map(D_n) of a disk D with n marked points. An isomorphism from Map(D_n) to B_n is given by evaluation of certain isotopies. In my talk I want to discuss an orbifold analogue. Therefore I will introduce orbifold braid groups and orbifold mapping class groups. In contrast to the classical analogue the evaluation map from the orbifold mapping class group onto the orbifold braid group has a non-trivial kernel. This has surprising consequences for the structure of the pure orbifold braid groups.

15:00 Coffee break

15:30 Bianca Marchionna (Bielefeld) Trees, buildings and their interactions

Abstract: It is a common approach to study the structure of groups by investigating how they act on geometric and combinatorial objects, e.g., trees or buildings. After briefly introducing the two structures, we will discuss a criterion for constructing trees from buildings due to F. Haglund and F. Paulin, and will sketch an alternative proof. Using the above-mentioned construction, one can produce new cohomological and simplicity results for groups acting Weyl transitively on buildings. Joint work with I. Castellano and T. Weigel.

Picture of the seminar.

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

Supported by Mathematics Münster