SEMINARIO TEORÍA DE GRUPOS

Quasi-Isometries for certain Right-Angled Coxeter Groups

Ponente: Alexandra Edletzberger (Universidad de Viena)

Fecha: Martes, 25 de abril de 2023 - 11:30

Lugar: Aula Gris 2, ICMAT

Resumen:

In the hunt for a solution to the Quasi-Isometry Problem within the class of right-angled Coxeter groups (RACGs) and between RACGs and right-angled Artin groups (RAAGs), we use a quasi-isometry invariant that is obtained by a certain splitting of the groups. In this talk, we introduce this splitting, the so-called Graph of Cylinders and the structure invariant it provides. We will give its construction for a large family of (in particular non-hyperbolic) RACGs that can be read off the presentation graph. This means that we can distinguish certain RACGs up to quasi-isometry just by comparing their presentation graphs. Then, we will compare the structure invariant of RACGs with the structure invariant of RAAGs and use it to distinguish these two classes up to QI.