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On the homotopy-symmetry of sphere bundles

Published online by Cambridge University Press:  24 October 2008

I. M. James
I. M. James
Affiliation:
Mathematical Institute, Oxford
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Extract

1. Introduction: Let B be a space and let E be an orthogonal (m + 1)-sphere bundle over B with projection p: E → B. Consider the fibre-preserving map T: E → E which is given by the antipodal transformation in each of the fibres. Following (4) we say that E is homotopy-symmetric if there exists a fibre-preserving homotopy of T into the identity map. Since T maps the fibres with degree (– 1)m this condition requires m to be even.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 2 , March 1971 , pp. 291 - 294
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

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