On Siebenmann periodicity
type: Item
instance of: scholarly article
title: On Siebenmann periodicity
zbMATH Open document ID: 0930.57028
author: Steven Hutt
published in: Pacific Journal of Mathematics
publication date: 2000-02-07T00:00:00Z
review text: Elements of the structure set \(S(M)\) of a compact \(n\)-dimensional topological manifold \(M\) are equivalence classes of simple homotopy equivalences \(h:N\to M\), where \(h\) restricts to a homeomorphism on \(\partial N\). Two maps \(h_i:N_i\to M\) of topological manifolds \(N_i\) are equivalent if there is a homeomorphism \(\phi:N_1\to N_2\) such that \(h_2\cdot\phi\) is homotopic (rel \(\partial\)) to \(h_1\). The author gives a topological construction of the Cappell-Weinberger exact sequence \(0\to S(M)\to S(M\times D^4,\partial)\to Z\) using mapping cylinder neighborhood techniques. He uses his theory of Poincaré sheaves to obtain a relation between the Cappell-Weinberger map and the algebraic form of Siebenmann periodicity.
Mathematics Subject Classification ID: 57Q10
zbMATH DE Number: 1344247
zbMATH Keywords: structure set of topological manifold
zbMATH Keywords: Cappell-Weinberger
reviewed by: Wolfgang Heil
MaRDI profile type: Publication
full work available at URL: pjm.1998.183.291
OpenAlex ID: W1979060915
DOI: 10.2140/PJM.1998.183.291
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description: scientific article; zbMATH DE number 1344247