Bielefeld-Münster Seminar
on Groups, Geometry and Topology

Date: January 28, 2019

Venue: Bielefeld University

The talks will take place in V2-210. Coffee will be served in the same room during the breaks.

Schedule

10:00 UhrBenjamin Brück
Free factors at infinity
11:00 UhrCoffee break
11:30 UhrYuri Santos
Soluble matrix groups and their finiteness lengths
12:30 UhrLunch break
14:00 UhrOlga Varghese
Abstract group homomorphisms between locally compact groups and discrete groups
15:00 UhrCoffee break
15:30 UhrNils Leder
Property FA for Automorphism Groups of small Graph Products
16:30 UhrEnd the of seminar

Abstracts

Benjamin Brück

Free factors at infinity

Borel and Serre constructed a compactification of symmetric spaces known as the Borel-Serre bordification. They showed that the topology at infinity of this structure can be described combinatorially by a rational Tits building. Outer space is a contractible simplicial complex on which Out(Fn), the outer automorphism group of the free group, acts cocompactly and with finite stabilisers. It is often seen as an Out(Fn)-analogue of symmetric spaces.

There is also an Out(Fn)-complex which shares many properties with buildings of type An, namely the free factor complex defined by Hatcher and Vogtmann. In this talk, I will explain how the free factor complex can be seen as "sitting at infinity" of Outer space, obtaining an analogue of the result of Borel and Serre.

This is based on joint work with Radhika Gupta (see arXiv:1810.09380).

Yuri Santos

Soluble matrix groups and their finiteness lengths

The finiteness length is a useful invariant which allows one to distinguish and describe groups to a certain degree. In this talk we recall the definition of the finiteness length and discuss the ongoing challenge of computing it for soluble linear groups, focusing on famous examples.

Olga Varghese

Abstract group homomorphisms between locally compact groups and discrete groups

We consider abstract group homomorphisms from l.c. groups into groups which are in the class

G={H | any torsion subgroup of H is finite and any abelian subgroup of H is finitely generated}.

We show that any abstract homomorphism f from a locally compact group into a group H, where H is in the class G, is continuous or the image of f lies in the normalizer of a finite non-trivial subgroup of H. In particular, any abstract homomorphism from a locally compact group into a right angled Artin group is continuous.

This is joint work with L. Kramer.

Nils Leder

Property FA for Automorphism Groups of small Graph Products

We discuss the question whether the automorphism group Aut(G) of a graph product of finite cyclic groups has Serre's property FA.

If we fix a prime power n=pk, k ≥ 1 and assume all vertex groups to be cyclic of order n, we can give a full classification for small graph products, i.e. graph products whose defining graph has at most 5 vertices.

The main tools involved are results on special graph products (free products, circles) and some reduction techniques. The latter use characteristic subgroups to reduce the question for a given graph product G to a graph product G' with a smaller number of vertices.

Last modified: Mon 04 Jan 2021, 12:05