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Poincaré duality and periodicity

John R Klein and William Richter
Algebraic & Geometric Topology 11 (2011) 1961–1985
DOI: 10.2140/agt.2011.11.1961
Abstract

We construct periodic families of Poincaré complexes, partially solving a question of Hodgson, and infinite families of Poincaré complexes whose top cell falls off after one suspension but which fail to embed in a sphere of codimension one. We give a homotopy theoretic description of the four-fold periodicity in knot cobordism.

Keywords
Poincaré complex, Hopf invariant, knot periodicity
Mathematical Subject Classification 2000
Primary: 57P10, 57Q45
Secondary: 55Q25, 55P91
References
Publication
Received: 8 July 2007
Revised: 7 March 2011
Accepted: 7 April 2011
Published: 30 June 2011
Authors
John R Klein
Department of Mathematics
Wayne State University
Detroit MI 48202
USA
William Richter
Department of Mathematics
Northwestern University
Evanston IL 60208
USA