Skip to main content

Group rings and hyperbolic geometry

Posted in
Grigori Avramidi
Mon, 22/04/2024 - 14:00 - 15:00
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

In the 60's Cohn showed that all ideals in the group algebra of a free group are free. Bass and Wall used this result to show that all two-dimensional complexes with free fundamental groups are standard: they are all homotopy equivalent to wedges of circles and 2-spheres. The goal of this talk is to describe recent results of this type for groups acting on hyperbolic spaces. I will discuss an algorithm showing that in the group algebra of a group acting on a hyperbolic space, ideals generated by ``few'' elements are free (where "few'' is a function of the minimal displacement of the action) and an application to complexity of cell decompositions of hyperbolic manifolds. Joint work with Thomas Delzant.

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A