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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1977-0442931-4

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