Kurt Gödel Research Center

On the limits in the space of marked groups

Talk held by Goulnara Arzhantseva (Mathematics, University of Vienna, Austria) at the KGRC Friday seminar on 2012‑04‑20.

Abstract

The space of marked groups provides a natural topological framework for studying the class of finitely generated groups as a whole (as an alternative to the investigation of specific classes, e.g. solvable groups). It plays a crucial role, for instance, in Gromov’s proof of the polynomial growth theorem and in Grigorchuk’s construction of, for any prime p, an uncountable family of 2-generated torsion p-groups with different types of intermediate growth. In this talk, we will focus on the amenability of the limit groups in this space.