The equivariant Serre spectral sequence as an application of a spectral sequence of Spanier |
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Authors: | Hannu Honkasalo |
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Affiliation: | Department of Mathematics, P.O. Box 4, FIN-00014 University of Helsinki, Helsinki, Finland |
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Abstract: | E.H. Spanier (1992) has constructed, for a cohomology theory defined on a triangulated space and locally constant on each open simplex, a spectral sequence whose E2-term consists of certain simplicial cohomology groups, converging to the cohomology of the space. In this paper we study a closed G-fibration ƒ: Y → X, where G is a finite group. We show that if the base-G-spaceX is equivariantly triangulated and Y is paracompact, then Spanier's spectral sequence yields an equivariant Serre spectral sequence for ƒ. The main point here is to identify the equivariant singular cohomology groups of X with appropriate simplicial cohomology groups of the orbit space X/G. |
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Keywords: | Serre spectral sequence Equivariant cohomology |
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