Abstract
If a group G operates on a topological space X, then one can define equivariant homology and cohomology groups, which can be thought of heuristic-ally as a “mixture” of H(G) and H(X). This equivariant theory provides a powerful tool for extracting homological information about G from the action of G on X. It is in this way, for example, that Quillen proved his theorem about the Krull dimension of H*(G, ℤp) for G finite (VI.9.8).
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© 1982 Springer-Verlag New York Inc.
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Brown, K.S. (1982). Equivariant Homology and Spectral Sequences. In: Cohomology of Groups. Graduate Texts in Mathematics, vol 87. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9327-6_8
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DOI: https://doi.org/10.1007/978-1-4684-9327-6_8
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