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The Kreck monoids l2q+1(ℤπ) detect s-cobordisms amongst certain bordisms between stably diffeomorphic 2q-dimensional manifolds and generalise the Wall surgery obstruction groups, . In this paper we identify l2q+1(ℤπ) as the edge set of a directed graph with vertices a set of equivalence classes of quadratic forms on finitely generated free ℤπ modules. Our main theorem computes the set of edges l2q+1(υ, υ′) ⊂ l2q+1(ℤπ) between the classes of the forms υ and υ′ via an exact sequence
Crowley et al. (Wed,) studied this question.