2 results
Quelques calculs de traces compactes et leurs transformées de Satake
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- Journal:
- Canadian Journal of Mathematics / Volume 60 / Issue 2 / 01 April 2008
- Published online by Cambridge University Press:
- 20 November 2018, pp. 412-442
- Print publication:
- 01 April 2008
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- Article
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Monoidal Functors, Acyclic Models and Chain Operads
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- Journal:
- Canadian Journal of Mathematics / Volume 60 / Issue 2 / 01 April 2008
- Published online by Cambridge University Press:
- 20 November 2018, pp. 348-378
- Print publication:
- 01 April 2008
-
- Article
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- You have access
- Export citation
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We prove that for a topological operad
$P$ the operad of oriented cubical singular chains, 
$C_{*}^{^{\text{ord}}}(P)$, and the operad of simplicial singular chains, 
${{S}_{*}}(P)$, are weakly equivalent. As a consequence, 
$C_{*}^{^{\text{ord}}}(P;\,\mathbb{Q})$ is formal if and only if 
${{S}_{*}}(P;\,\mathbb{Q})$ 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.
