Cappell and Weinberger gave a
geometric interpretation of the Siebenmann periodicity phenomena. This
near-periodicity on the structure sets of topological manifolds was originally
demonstrated in an indirect way from the periodicity of the simply-connected
quadratic L-groups, see Nicas and Siebenmann (1977). In particular it was shown for
a topological manifold M, dimM ≥ 5, with structure set S(M), that there is an
exact sequence
Cappell and Weinberger recovered the inclusion in the exact sequence directly by a
geometric construction on homotopy equivalences of topological manifolds. More
precisely, they lay the foundations for such a construction since the tools employed in
Cappell and Weinberger were of the PL-category and so inappropriate for general
topological manifolds.
