Geometry and Topology of Artin Groups

Basic data for this project

Description

Groups are mathematical tools designed to encode symmetry. Over the years it became apparent that groups are not mere tools - they are interesting objects in their own right. And even though they are of an algebraic nature, they can be studied from topological and geometric viewpoints. One particular family of groups appearing throughout mathematics, as well as in seemingly remote applications like robotics or cryptography, is the family of braid groups. Such groups have been very successfully studied, and are amenable to various approaches stemming from all corners of pure mathematics. Braid groups are but one family in a very rich class that is central to our project - Artin groups. We want to focus on five representative classes of Artin groups: those of type FC, of classical type, of Euclidean type, as well as two-dimensional and right-angled ones. For each class we want to investigate a different geometric or topological question. More specifically, we want to look into the Farrell-Jones conjecture, higher generation by families of parabolic subgroups, Nielsen realisation and possible actions by topological groups. The project will bring together German and Polish researchers, with their individual expertise and unique perspectives, to shed new light on Artin groups, and expand our knowledge of this rich class.