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A Generalization of “Concordance of PL-Homeomorphisms of Sp × Sq

Published online by Cambridge University Press:  20 November 2018

J. P. E. Hodgson
J. P. E. Hodgson*
Affiliation:
University of Pennsylvania, Philadelphia, Pennsylvania
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Let Mm be a closed PL manifold of dimension m. Then a concordance between two PL-homeomorphisms h0, h1:M → M is a PL-homeomorphismH: M × I → M × I such that H|M × 0 = h0 and H|M × 1 = h. Concordance is an equivalence relation and in his paper [2], M. Kato classifies PL-homeomorphisms of Sp × Sq up to concordance. To do this he treats first the problem of classifying those homeomorphisms that induce the identity in homology, and then describes the automorphisms of the cohomology ring that can arise from homeomorphisms of Sp × Sq. In this paper we show that for sufficiently connected PL-manifolds that embed in codimension 1, one can extend Kato's classification of the homeomorphisms that induce the identity in homology.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 3 , June 1972 , pp. 426 - 431
Copyright
Copyright © Canadian Mathematical Society 1972

References

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