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KSO-Groups for 4-Dimensional CW-Complexes

Published online by Cambridge University Press:  22 January 2016

Seiya Sasao  and
Yutaka Ando
Seiya Sasao
Affiliation:
Department of Mathematics, Tokyo Institute of Technology
Yutaka Ando
Affiliation:
Department of Mathematics, Tokyo Institute of Technology
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In this paper we shall determine KSO-groups for 4-dimensional CW-complexes by their cohomology rings. We denote by KSO(X) the group of orientable stable vector bundles over X. In 1959 A. Dold and H. Whitney [1] gave the classification of SO(n)-bundles over a 4-complex. It seems, however, to the authors that group structures of them are unknown. We shall give another definition of the difference bundles defined in [1], and we determine the group structure of KSO(X).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 42 , March 1971 , pp. 23 - 29
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Dold, A. and Whitney, H., “Classifications of oriented sphere bundles over a 4-complex,” Ann. of Math., 69 (1959), 667–677.CrossRefGoogle Scholar