Journal article

The additivity of the rho-invariant and periodicity in topological surgery

Diarmuid Crowley, Tibor Macko

Algebraic & Geometric Topology | GEOMETRY & TOPOLOGY PUBLICATIONS | Published : 2011

Abstract

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 as defined by Ranicki. If dim(M) = 2d - 1, M is oriented and M is equipped with a map to the classifying space of a finite group G, then the reduced p -invariant defines a function, p: S(M)! QRG-d, to a certain subquotient of the complex representation ring of G. We show that the function p̃ is a homomorphism when 2d - 1 > 5. Along the way we give a detailed proof that a geometrically defined map due to Cap-pell and Weinberger realises the 8-fold Siebenmann periodicity map in topological surgery.

University of Melbourne Researchers

Grants

Awarded by Geometrische Strukturen in der Mathematik, Munster


Funding Acknowledgements

The second author was supported by SFB 478 Geometrische Strukturen in der Mathematik, Munster.