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.