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A Composition Formula for Manifold Structures

The structure set STOP (M) of an n-dimensional topological manifold M for n > 5 has a homotopy invariant functorial abelian group structure, by the algebraic version of the Browder-Novikov-Sullivan-Wall surgery theory. An element (N, f) ∈ STOP (M) is an equivalence class of n-dimensional manifolds N with a homotopy equivalence f : N → M . The composition formula is that (P, fg) = (N, f) + f∗(P, g) ∈ STOP (M) for homotopy equivalences g : P → N , f : N → M . The formula is required for a paper of Kreck and Lück.