A natural goal of geometric group theory is to understand the algebraic properties of a group via geometry. The far-reaching work of Dahmani-Guirardel-Osin and recent work of Clay-Mangahas-Margalit provide geometric approaches to the study of the normal closure of a subgroup in a large ambient group. In particular, their work gives conditions under which the normal closure is a free product. I will talk about recent work that aims to unify their results and gives a significantly shorter proof of the theorem of DGO. This is joint work with M. Bestvina, R. Dickmann, S. Kwak, P. Patel, and E. Stark.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
