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Volume 183 No. 2 (1998), 291-303
Steven Hutt
On Siebenmann Periodicity
Abstract:
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,
dim M > 4, with structure set S(M), that there is an exact sequence
0 -> S(M) -> S(M x D4,boundary) -> Z.
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.
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