2010/11/28 by Kathryn Hess, Hess, Kathryn
Mathematics · #18G30 #18G35 #18G55 #55P35 #55P40 #55R20 (Primary) 18D50 #55U05 #55U10 #57T05 (Secondary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1011.6092
openalex publication_date 2010/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.