Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-25T08:49:19.545Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Hodgson, J. P. E., Obstructions to concordance for thickenings, Inv. Math. 5 (1968), 292–316.Google Scholar
2. Kato, M., A concordance classfication of PL homeomorphisms of Sp × Sq; Topology 8 (1969), 371–383.Google Scholar
3. Rourke, C. P. and Sanderson, B. J., ∆-sets. I, Preprint (Warwick, 1969).Google Scholar
4. Stallings, J., Embedding homotopy types, Preprint (Princeton, 1966).Google Scholar
5. Wall, C. T. C., Classification problems in differential topology IV: thickenings, Topology 5 (1965), 73–94.Google Scholar
6. Zeeman, E. C., The Poincaré conjecture n≥5, Topology of 3-manifolds, Ed. Fort, M. K.., pp. 198–204 (Prentice Hall, 1962).Google Scholar
7. Zeeman, E. C., Seminar on combinatorial topology. III (I. H. E. S., 1963).Google Scholar