KIT | MATH | IAG | RG Topology | Topology and Geometric Group Theory | Talks - On the nature of subgroups of direct products of free groups

Date:
02.12.21
Speaker:
Claudio Llosa Isenrich
Time:
16:00 - 17:30
Abstract

By the Nielsen-Schreier Theorem every subgroup of a free group is free. This raises the question if subgroups of direct products of free groups can be described in similarly simple terms. This turns out to be far from true: even in a direct product of two non-abelian free groups there are uncountably many pairwise non-isomorphic finitely generated subgroups. However, if we restrict our attention finitely presented subgroups, the situation becomes much nicer, albeit still far from trivial, as the Stallings--Bieri groups show. I will give an introduction to this interesting class of groups, with a particular focus on their finiteness properties and (time-permitting) their Dehn functions.