Vol. 80, No. 1, 1979

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Homotopy conditions which detect simple homotopy equivalences

Thomas Ashland Chapman

Vol. 80 (1979), No. 1, 13–46
Abstract

Let X, Y , and K be compact polyhedra, let p : Y × K Y be the projection map, and let f : X Y × K be a homotopy equivalence which has a homotopy inverse g : Y × K X along with homotopies fg id, gf id such that p(fg id) and pf(gf id) are small homotopies. In this paper we prove that if π1 of each component of K is free abelian, then f must be a simple homotopy equivalence.

Mathematical Subject Classification 2000
Primary: 57Q10
Milestones
Received: 7 March 1977
Revised: 13 June 1978
Published: 1 January 1979
Authors
Thomas Ashland Chapman