Applications of bundle map theory

Gottlieb, Daniel Henry

doi:10.1090/S0002-9947-1972-0309111-X

Applications of bundle map theory
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by Daniel Henry Gottlieb

Trans. Amer. Math. Soc. 171 (1972), 23-50

DOI: https://doi.org/10.1090/S0002-9947-1972-0309111-X

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Abstract:

This paper observes that the space of principal bundle maps into the universal bundle is contractible. This fact is added to I. M. James’ Bundle map theory which is slightly generalized here. Then applications yield new results about actions on manifolds, the evaluation map, evaluation subgroups of classifying spaces of topological groups, vector bundle injections, the Wang exact sequence, and $H$-spaces.

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