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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the $ p$-primary obstructions to finding a cross-section


Author: Robert Rigdon
Journal: Proc. Amer. Math. Soc. 47 (1975), 243-250
MSC: Primary 55G40
MathSciNet review: 0362308
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Abstract: Let $ q:T \to B$ be a (weak) fibration, and let $ p$ be an odd prime. In this paper, we show that the existence of a fiber-preserving map $ A:T \to T$ having certain properties implies that the $ p$-primary obstructions to a cross-section of $ q$ vanish. Assuming that $ q:T \to B$ has a cross-section, we prove a related theorem which bears on the problem of enumerating the homotopy classes of cross-sections of $ q$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0362308-3
Keywords: Fiber space, Stiefel bundle, cross-section, obstruction, Postnikov system
Article copyright: © Copyright 1975 American Mathematical Society