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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Approximating groups of bundle automorphisms by loop spaces

Author: Roberto Bencivenga
Journal: Trans. Amer. Math. Soc. 285 (1984), 703-715
MSC: Primary 55R10; Secondary 55P35
MathSciNet review: 752499
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Abstract: D. H. Gottlieb proved in 1972 that the group of automorphisms of a numerable $ G$-bundle $ p:X \to B$ is weakly homotopy equivalent to $ \Omega \;\operatorname{Map}(B,{B_G};k)$, where $ k:B \to {B_G}$ is a classifying map for $ p$. We refine this classical result by constructing a genuine homotopy equivalence between these two spaces which is natural with respect to numerable bundle morphisms, can be generalized to fibre bundles, and can be interpreted as a natural isomorphism between two suitably defined functors.

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Keywords: Bundle automorphism group, loop space, homotopy equivalence, natural isomorphism
Article copyright: © Copyright 1984 American Mathematical Society

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