Quasi-isometric rigidity of graphs of surface groups
Alex Taam (Stevens)
Abstract: A group is a graph of rigid surface groups, or a grsg-group, if it is word hyperbolic and it has a cyclic JSJ decomposition with only rigid type non-cyclic vertex groups, all of which are the fundamental groups of closed surfaces. In this talk, I will discuss recent work with Nicholas Touikan, showing that these groups are quasi-isometrically rigid, in that every quasi-isometry class of grsg-groups consists of a single commensurability class. I will also survey some related results and directions of continuing inquiry.