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Transactions of the American Mathematical Society

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



Fibrations of classifying spaces

Authors: Kenshi Ishiguro and Dietrich Notbohm
Journal: Trans. Amer. Math. Soc. 343 (1994), 391-415
MSC: Primary 55R35
MathSciNet review: 1231336
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Abstract: We investigate fibrations of the form $Z \to Y \to X$, where two of the three spaces are classifying spaces of compact connected Lie groups. We obtain certain finiteness conditions on the third space which make it also a classifying space. Our results allow to express some of the basic notions in group theory in terms of homotopy theory, i.e., in terms of classifying spaces. As an application we prove that every retract of the classifying space of a compact connected Lie group is again a classifying space.

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Keywords: Classifying space, mapping spaces, <I>p</I>-completion, Lie groups, universal covering, instable Adams operation genus
Article copyright: © Copyright 1994 American Mathematical Society