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Proceedings of the American Mathematical Society

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

 

 

The commutator subgroup of a free topological group need not be projective


Author: Francis Clarke
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1976-0404512-2
Keywords: Free topological group, commutator subgroup, projective topological group, Serre spectral sequence
Article copyright: © Copyright 1976 American Mathematical Society