Vera Tonic -- Asymptotic dimension and some applications to geometric (approximate) group theory
Author information
- Vera Tonic
- University of Rijeka, Croatia
Abstract:
A well-known theorem from geometric group theory, proven by S. Buyalo and N. Lebedeva in 2007, states that for a hyperbolic group \(G\), the equality asdim \(G = \dim (\partial G) + 1\) holds.
In this talk, we will review the notion of asymptotic dimension (asdim) for metric spaces, and, in particular, show how asdim is defined on groups, as well as see the basics about hyperbolic groups and their boundaries. We will also introduce the concept of approximate group, based on T. Tao’s definition of approximate subgroups from 2008, and see how to define asdim and hyperbolicity of approximate groups.
We will then show that Buyalo-Lebedeva’s theorem can be generalized to hyperbolic approximate groups.
This is joint work with Tobias Hartnick of KIT, Karlsruhe.