Exotic relation modules and homotopy types for certain 1–relator groups

Abstract

Using stably free non-free relation modules we construct an infinite collection of 2-dimensional homotopy types, each of Euler-characteristic one and with trefoil fundamental group. This provides an affirmative answer to a question asked by Berridge and Dunwoody We also give new examples of exotic relation modules. We show that the relation module associated with the generating set fx; y 4 g for the Baumslag-Solitar group hx; y j xy 2 x 1 D y 3 i is stably free non-free of rank one.