Séance Séminaire

Séminaire Gaston Darboux

On the isomorphism problem for procountable groups

We present a recent result, obtained jointly with Su Gao and André Nies, on the complexity of the isomorphism problem for procountable groups, i.e., topological groups arising as inverse limits of countable groups. Specifically, we show that topological isomorphism on 2-nilpotent procountable groups is not classifiable by countable structures in the sense of Borel reducibility. We will also discuss some open questions and group-theoretic constructions arising from this work.