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 [J. London Math. Soc. 19 (1979) 433–436]. We also give new examples of exotic relation modules. We show that the relation module associated with the generating set for the Baumslag–Solitar group is stably free non-free of rank one.
"Exotic relation modules and homotopy types for certain 1–relator groups." Algebr. Geom. Topol. 6 (5) 2163 - 2173, 2006. https://doi.org/10.2140/agt.2006.6.2163