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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Fibrations of classifying spaces
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by Kenshi Ishiguro and Dietrich Notbohm PDF
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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 391-415
  • MSC: Primary 55R35
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1231336-4
  • MathSciNet review: 1231336