Multiplicative structure in equivariant cohomology

Details Multiplicative structure in equivariant cohomology Multiplicative structure in equivariant cohomology

2010-11-28

arxiv.org/abs/1011.6092v2

Mathematics

Algebraic Topology

28 pages. Final version (cosmetic changes, slight reorganization), to appear in JPAA

Scientific paper

We introduce the notion of a strongly homotopy-comultiplicative resolution of a module coalgebra over a chain Hopf algebra, which we apply to proving a comultiplicative enrichment of a well-known theorem of Moore concerning the homology of quotient spaces of group actions. The importance of our enriched version of Moore's theorem lies in its application to the construction of useful cochain algebra models for computing multiplicative structure in equivariant cohomology. In the special cases of homotopy orbits of circle actions on spaces and of group actions on simplicial sets, we obtain small, explicit cochain algebra models that we describe in detail.

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