On the homotopy-symmetry of sphere bundles
Published online by Cambridge University Press: 24 October 2008
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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