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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The classifying space of a permutation representation


Author: James V. Blowers
Journal: Trans. Amer. Math. Soc. 227 (1977), 345-355
MSC: Primary 55F35; Secondary 20C30
MathSciNet review: 0442931
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Abstract: In this article the concept of classifying space of a group is generalized to a classifying space of an arbitrary permutation representation. An example of this classifying space is given by a generalization of the infinite join construction that defines the standard example of a classifying space of a group. In a previous paper of the author, the join of two permutation representations was defined, and it was shown that the cohomology ring of the join was trivial. In this paper the classifying space of the join of two permutation representations is shown to be the topological join of the two classifying spaces and from this the triviality of the cup-product is derived topologically.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0442931-4
PII: S 0002-9947(1977)0442931-4
Keywords: Classifying space, permutation representation, join, cell complexes, cohomology ring, cup-products, equivariantly acyclic carriers, equivariantly proper maps, contractible spaces
Article copyright: © Copyright 1977 American Mathematical Society