Multiplicative structure in equivariant cohomology
release_ki2y2tgo7bakxdgpabquvle4pq
by
Kathryn Hess
2011
Abstract
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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