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On Siebenmann periodicity

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