Fibrations of classifying spaces

Ishiguro, Kenshi; Notbohm, Dietrich

doi:10.1090/S0002-9947-1994-1231336-4

Fibrations of classifying spaces
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Trans. Amer. Math. Soc. 343 (1994), 391-415 Request permission

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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