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Monoidal functors, acyclic models and chain operads
Guillén Santos, Francisco; Navarro, Vicenç (Navarro Aznar); Pascual Gainza, Pere; Roig Martí, Agustín
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
We prove that for a topological operad P the operad of oriented cubical chains, Cord ¤ (P), and the operad of singular chains, S¤(P), are weakly equivalent. As a consequence, Cord ¤ (P;Q) is formal if and only if S¤(P;Q) is formal, thus linking together some formality results spread in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give di®erent variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets de¯ned by R-simplicial di®erential graded algebras.
Algebraic topology
Monoidal functors
Acyclic models
Chain operads
Topologia algebraica
Classificació AMS::55 Algebraic topology
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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