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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The commutator subgroup of a free topological group need not be projective
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by Francis Clarke PDF
Proc. Amer. Math. Soc. 57 (1976), 354-356 Request permission

Abstract:

It is shown that the commutator subgroup of the free topological group on the $n$-sphere is, for $n > 1$, not projective and hence not free topological. The proof depends on the computation of the $\bmod 2$ cohomology ring of the classifying space of the commutator subgroup.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 57 (1976), 354-356
  • MSC: Primary 22A05
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0404512-2
  • MathSciNet review: 0404512