Poincaré duality and periodicity

Klein, John R; Richter, William

doi:10.2140/agt.2011.11.1961

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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

Volume 11, issue 4 (2011)