The growth of groups, with application to Thompson's group F

Abstract. We have developed a variety of algorithms to generate the cogrowth series of a number of finitely-presented infinite groups. We develop methods to determine the asymptotics of the cogrowth series. As a result we provide the strongest numerical evidence yet that Thompson's group F is not amenable. We also analyse the behaviour of the Navas-Brin group B.

This is joint work with Andrew Elvey Price.