Speaker: Martin Bridson

Abstract:
I shall discuss recent results concerning the classification of finitely presented, residually free groups, giving explicit examples and useful characterisation theorems.

I shall sketch the proof that an arbitrary finitely-generated residually-free group either has a subgroup of finite index with a homology group that is not finitely generated, or else is virtually a direct product of fully-residually free (limit) groups.

As time allows, I shall:
(1) Describe the Bieri-Neumann-Strebel invariants of direct products of limit groups;
(2) prove that the membership (Magnus) problem is solvable for suchgroups;
(3) explain why all finitely presented subgroups are closed in the profinite topology.
(4) Solve the conjugacy problem for finitely presented residually-free groups.

This is joint work with (in various combinations) Howie, Miller, Short and Wilton.