Seminario teoría de grupos UAM-ICMAT

Miercoles 27 de Noviembre, 12:30, Aula 520, Modulo 17, Ciencias, UAM

Levi Sledd (Vanderbilt University)

Title: Assouad-Nagata dimension of $C'(1/6)$ groups.
Abstract: Asymptotic dimension is a coarse invariant of metric spaces, introduced by Gromov in 1993 as a large-scale analogue of topological dimension. A related concept is that of Assouad-Nagata dimension, a quasi-isometry invariant which is bounded below by asymptotic dimension. Historically, these two invariants have been hard to distinguish among finitely generated groups. In this talk, we show that any finitely generated $C'(1/6)$ group has Assouad-Nagata dimension at most $2$. Using this result we show how to construct, for any $n,k in mathbb N$ with $n geq 3$, a finitely generated group of asymptotic dimension $n$ and Assouad-Nagata dimension $n+k$.