The strong profinite genus can be infinite
Martin Bridson (University of Oxford)
Wednesday 6th November, 2013 16:00-17:00 Maths 204
In 2004, Bridson and Grunewald constructed the first examples of pairs of finitely presented residually finite groups u:H --> G so that H is not isomorphic to G but the inclusion induces an isomorphism of profinite completions (i.e. matches the finite quotients of H and G bijectively). At the time they were unable to prove that, for fixed G, there can be infinitely many non-isomorphic H with this property. It will be proved in this talk that there can indeed be such an infinitude. The proof involves recent advances in the understanding of how to present fibre products, some Bass-Serre theory, and a new twist on the difficult problem of deciding when two finite generating sets for a group are Nielsen equivalent.