Geometric Group Theory Seminar - Rachel Skipper

Title: Finiteness Properties for Simple Groups

Speaker: Rachel Skipper, The Ohio State University

Abstract: A group is said to be of type $F_n$ if it admits a classifying space with compact $n$-skeleton. We will consider the class of R\"{o}ver-Nekrachevych groups, a class of groups built out of self-similar groups and Higman-Thompson groups, and use them to produce a simple group of type $F_{n-1}$ but not $F_n$ for each $n$. These are the first known examples for $n\geq 3$. As a consequence, we find the second known infinite family of quasi-isometry classes of finitely presented simple groups.