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Homology of Deleted Products of Contractible 2-Dimensional Polyhedra. II

Published online by Cambridge University Press:  20 November 2018

C. W. Patty
C. W. Patty*
Affiliation:
The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina ; Virginia Polytechnic Institute, Blacksburg, Virginia
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The deleted product space X* of a space X is X × X — △. In (4), I computed the homology groups of the deleted product of a polyhedron in a subcollection (see §2 of this paper for the definition of ) of the finite, contractible, 2-dimensional polyhedra. In the present paper, I show that there is an infinite subcollection of such that the deleted product of each member of has the homotopy type of the 2-sphere.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 842 - 854
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This paper was presented to the American Mathematical Society on January 25, 1967. This research was partially supported by NSF Grant GP-7943.

References

1. Hu, S. T., Isotopy invariants of topological spaces, Proc. Roy. Soc. (London), Ser. A 255 1960) 331–366.Google Scholar
2. Patty, C. W., The fundamental group of certain deleted product spaces, Trans. Amer. Math. Soc. 105 (1962), 314–321.Google Scholar
3. Patty, C. W., Isotopy classes of imbeddings Trans. Amer. Math. Soc. 128 (1967), 232–247.Google Scholar
4. Patty, C. W., Homology of deleted products of contractible 2-dimensional polyhedra. I, Can. J. Math. 20 (1968), 416–441.Google Scholar