The Additivity of the Ρ-invariant and Periodicity in Topological Surgery
نویسندگان
چکیده
For a closed topological manifold M with dim(M) ≥ 5 the topological structure set S(M) admits an abelian group structure which may be identified with the algebraic structure group of M defined by Ranicki. If dim(M) = 2d−1, and the manifoldM is oriented and equipped with a map to the classifying space of a finite group G, then the reduced ρ-invariant defines a function ρ̃ : S(M)→ QR d Ĝ to a certain sub-quotient of the complex representation ring of G. We show that the function ρ̃ is a homomorphism when 2d− 1 ≥ 5. Along the way we give a detailed proof that a geometrically defined map due to Cappell and Weinberger realises the 8-fold Siebenmann periodicity map in topological surgery.
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