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 [1]. We also give new examples of exotic relation modules. We show that the relation module associated with the generating set {x, y 4 } for the Baumslag-Solitar group x, y | xy 2 x −1 = y 3 is stably free non-free of rank one. 57M20; 57M05
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