Four manifold topology and groups of polynomial growth

Richard Andrew Stong

Vol. 157 (1993), No. 1, 145–149

DOI: 10.2140/pjm.1993.157.145

Abstract

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 π₁(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.

Mathematical Subject Classification 2000

Primary: 57N13

Secondary: 57R65, 57R80

Milestones

Received: 3 September 1991

Revised: 5 November 1991

Published: 1 January 1993