Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/34464
Title: | Monoidal functors, acyclic models and chain operads |
Author: | Guillén Santos, Francisco Navarro, Vicenç (Navarro Aznar) Pascual Gainza, Pere Roig, Agustí |
Keywords: | Àlgebra homològica Topologia algebraica Homological algebra Algebraic topology |
Issue Date: | 1-Apr-2008 |
Publisher: | Canadian Mathematical Society |
Abstract: | We prove that for a topological operad $P$ the operad of oriented cubical singular chains, $C^{\ord}_\ast(P)$, and the operad of simplicial singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{\ord}_\ast(P\nsemi\mathbb{Q})$ is formal if and only if $S_\ast(P\nsemi\mathbb{Q})$ is formal, thus linking together some formality results which are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give different variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets defined by $R$-simplicial differential graded algebras. |
Note: | http://dx.doi.org/10.4153/CJM-2008-017-7 |
It is part of: | Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 2008, vol. 60, p. 348-378 |
URI: | http://hdl.handle.net/2445/34464 |
Related resource: | http://dx.doi.org/10.4153/CJM-2008-017-7 |
ISSN: | 0008-414X |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
531385.pdf | 495.09 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.