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Homotopy classification of connected sums of sphere bundles over spheres, I

Published online by Cambridge University Press:  22 January 2016

Hiroyasu Ishimoto
Hiroyasu Ishimoto*
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University
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In the classification problems of manifolds, the connected sums of sphere bundles over spheres appear frequently. In fact, the manifolds with certain tangential and homotopy properties come to such connected sums (cf. Tamura [15], [16], Ishimoto [6], [8], [9]). Motivated by those, in this paper and the subsequent paper, we classify connected sums of sphere bundles over spheres up to homotopy equivalence by extending the results of I. M. James and J. H. C. Whitehead [10], [11], which correspond to the case that the connected sums of the above happen to be single sums. We also use Wall [17] in the case when the fibres and the base spaces of bundles are same dimensional.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 83 , October 1981 , pp. 15 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

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