Four manifold topology and groups of polynomial growth (Q811620)

In this paper we present a new proof that groups of polynomial growth are ``good'' in the sense of Freedman and Quinn. It follows from the results of Freedman that the five-dimensional \(s\)-cobordism theorem and the surgery exact sequence in dimension four hold for \(\pi_ 1(M)\) of polynomial growth. In the processes, we will give a slightly more efficient procedure for grope height raising and a slightly different procedure for using the grope height to kill fundamental group images.