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2011 The additivity of the $\rho$–invariant and periodicity in topological surgery
Diarmuid Crowley, Tibor Macko
Algebr. Geom. Topol. 11(4): 1915-1959 (2011). DOI: 10.2140/agt.2011.11.1915

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)=2d1, M is oriented and M is equipped with a map to the classifying space of a finite group G, then the reduced ρ–invariant defines a function,

ρ̃:S(M)RĜ(1)d,

to a certain subquotient of the complex representation ring of G. We show that the function ρ̃ is a homomorphism when 2d15.

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.

Citation

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Diarmuid Crowley. Tibor Macko. "The additivity of the $\rho$–invariant and periodicity in topological surgery." Algebr. Geom. Topol. 11 (4) 1915 - 1959, 2011. https://doi.org/10.2140/agt.2011.11.1915

Information

Received: 9 February 2010; Revised: 30 March 2011; Accepted: 31 March 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1242.57017
MathSciNet: MR2826928
Digital Object Identifier: 10.2140/agt.2011.11.1915

Subjects:
Primary: 57R65, 57S25

Rights: Copyright © 2011 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2011
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