Bielefeld-Münster Seminar
on Groups, Geometry and Topology

Date: 13 July 2018

Venue: University of Münster, Einsteinstraße 62

The talks will be in room SR0 in the main building. Tea will be served in the same room during the breaks.

Schedule

10:00Olga Varghese
Coherence in graph products
11:00Coffee break
11:30Jeroen Schillewaert
On exceptional homogeneous compact geometries of type C3
12:30Lunch break
14:00Sophiane Yahiatene
Coxeter transformations of extended Weyl groups
15:00Coffee break
15:30Eduard Schesler
Sphericity of complexes associated to spherical buildings
16:30End the of seminar

Abstracts

Olga Varghese

Coherence in graph products

A groups G is coherent if every finitely generated subgroup of G is finitely presented. We prove that many graph products are coherent.

Jeroen Schillewaert

On exceptional homogeneous compact geometries of type C3

Tits introduced geometries of Coxeter type, which locally are buildings.

Flag-transitive finite geometries of type C3 have been classified by Aschbacher and Yoshiara. Such a geometry is either a building, or it is isomorphic with the Neumaier geometry on seven points. In the compact connected case a similar classification has been obtained by Kramer and Lytchak, such a geometry is either covered by a building, or it is isomorphic to one of two exceptional geometries. We will provide a uniform construction for these two exceptional geometries using composition algebras and show their simple connectedness. ​

Sophiane Yahiatene

Coxeter transformations of extended Weyl groups

Extended Weyl groups occur in various branches of mathematics, for example in representation theory of finite dimensional algebras and in singularity theory. There, the Coxeter transformations play an important role in understanding the underlying structures. After a short motivation and necessary definitions, we will present important properties and state some open problems and also progress in solving them.

Eduard Schesler

Sphericity of complexes associated to spherical buildings

Every spherical building Δ admits a canonical CAT(1)-metric d such that every apartment Σ of Δ is isometric to the unit sphere Sdim(Δ) with respect to d. Hence for any point p ∈ Σ we can define the hemisphere Hp ⊂ Σ centered at p. Let ρΣ,C: Δ → Σ be the canonical retraction with respect to some chamber C of Σ. We formulate a conjecture concerning the sphericity of the subspace ρ-1Σ,C(Hp) ⊂ Δ and present some known and some new affirmative results for that conjecture.

Connections

There is an ICE connection leaving in Bielefeld at 8:22 and arriving in Münster at 9:22. There is also a local train connection leaving in Bielefeld at 7:59 and arriving in Münster at 9:17.

The following busses go from Münster station to Coesfelder Kreuz in the relevant period:

Last modified: Mon 04 Jan 2021, 12:05