Date: 22 Feburary 2017

Venue: Bielefeld University

All talks will take place in V3-201. Coffee will be served in the same room during the breaks.

If you have questions, please contact the organizer.

Schedule

10:00 Uhr	Yuri Santos
	Finite presentability of parabolics in Chevalley groups
11:00 Uhr	Coffee break
11:30 Uhr	Eduard Schesler
	Bounded subgroups of relatively finitely presented groups
12:30 Uhr	Lunch break
14:00 Uhr	Cora Welsch
	Contractibility of coset posets of finite index subgroups of finitely generated infinite groups
15:00 Uhr	Coffee break
15:30 Uhr	Nils Leder
	Automorphisms of Free Products and Property (FA)
16:30 Uhr	End the of seminar

Abstracts

Yuri Santos

Finite presentability of parabolics in Chevalley groups

Given a parabolic subgroup P = UL of a universal Chevalley group, we consider the question of how do presentations of P and of its Levi factor L relate. We shall obtain a criterion, based on the underlying root system, to determine a "nice" relative presentation of P with respect to L via generators and relators à la Steinberg. Invoking results of Behr, Bux and others, we are able to classify finitely presentable S-arithmetic subgroups of parabolics of almost simple algebraic groups in many new cases.

Eduard Schesler

Bounded subgroups of relatively finitely presented groups

We begin by introducing relatively finitely presented groups which generalize relatively hyperbolic groups. Since a relatively finitely presented group G is equipped with a generating set X which may contain infinite parabolic subgroups, it makes sense to study infinite bounded subgroups of G. We will show that every infinite bounded subgroup of G is already conjugated into a parabolic subgroup if the relative Dehn function of G is well defined.

Cora Welsch

Contractibility of coset posets of finite index subgroups of finitely generated infinite groups

I have proved that the nerve and the order complexes of the poset of the coset of all finite index subgroups are contractible for many important classes of finitely generated infinite groups. Thus the upcoming question was: Are there groups such that the nerve and order complexes are not contractible? We can now answer this question in the affirmative and give examples.

Nils Leder

Automorphisms of Free Products and Property (FA)

A group H is said to have Serre's property (FA) if any action of H on a tree T has a global fix point, i.e. there is a vertex v ∈ V(T) such that h(v)=v holds for all h ∈ H.

Let n, m ∈ ℕ,n,m ≥ 2 and G=ℤ/nℤ * … * ℤ/nℤ denote the free product of m copies of the finite cyclic group ℤ/nℤ. I am interested in the question wether the automorphism group Aut(G) has property (FA).

In order to explore the structure of Aut(G), we consider so called n-bases which are special generating sets of G that feature some properties analogous to a basis of a free group. These n-bases give rise to a simplicial complex Δ on which Aut(G) acts in a natural way. If Δ turns out to be a chamber complex, the action gives us a nice generating set for Aut(G).

In particular, this implies that Aut(G) does not have property (FA) in the case of m=2 free factors.

Last modified: Mon 04 Jan 2021, 12:05