Algebra Seminar: talk by Olga Varghese

On Wednesday the 18th of May 2022, Olga Varghese (Otto von Guericke University Magdeburg) virtually visited the Charlotte Scott Centre for Algebra in Lincoln and Lund University and gave a talk “Automatic continuity-prominent examples in geometric group theory”.

Abstract: In the category of locally compact Hausdorff groups LCG one has to distinguish between algebraic morphisms and algebraic and continuous morphisms. Let Epi(L,G) be the set of surjective group homomorphisms and cEpi(L,G) the subset consisting of continuous surjective group homomorphisms. The question we address is the following: Under which conditions on the discrete group G does the equality Epi(LCG,G)=cEpi(LCG,G) hold? In particular, we show that any surjective group homomorphism from a locally compact Hausdorff group into the automorphism group of a right-angled Artin group Aut(A_\Gamma) is continuous.