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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some weak equivalences for classifying spaces


Author: Solomon M. Jekel
Journal: Proc. Amer. Math. Soc. 90 (1984), 469-476
MSC: Primary 57R32; Secondary 55P10
MathSciNet review: 728371
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Abstract: For topological categories $ \mathcal{C}$ with fractions we give a model for the loops on the classifying space $ \Omega B\mathcal{C}$ as a simplicial group which generalizes the fact that $ \Omega B\mathcal{C} = \mathcal{C}$ when $ \mathcal{C}$ is a topological group. This construction is applied to give some well-known, and some new, examples of weak equivalences between classifying spaces arising in the theory of foliations.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0728371-8
PII: S 0002-9939(1984)0728371-8
Article copyright: © Copyright 1984 American Mathematical Society