Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300190312> ?p ?o ?g. }
Showing items 1 to 57 of
57
with 100 items per page.
- W4300190312 abstract "We establish that $E_n$-operads satisfy a rational intrinsic formality theorem for $ngeq 3$. We gain our results in the category of Hopf cooperads in cochain graded dg-modules which defines a model for the rational homotopy of operads in spaces. We consider, in this context, the dual cooperad of the $n$-Poisson operad $mathsf{Pois}_n^c$, which represents the cohomology of the operad of little $n$-discs $mathsf{D}_n$. We assume $ngeq 3$. We explicitly prove that a Hopf cooperad in cochain graded dg-modules $mathsf{K}$ is weakly-equivalent (quasi-isomorphic) to $mathsf{Pois}_n^c$ as a Hopf cooperad as soon as we have an isomorphism at the cohomology level $H^*(mathsf{K})simeqmathsf{Pois}_n^c$ when $4nmid n$. We just need the extra assumption that $mathsf{K}$ is equipped with an involutive isomorphism mimicking the action of a hyperplane reflection on the little $n$-discs operad in order to extend this formality statement in the case $4mid n$. We deduce from these results that any operad in simplicial sets $mathsf{P}$ which satisfies the relation $H^*(mathsf{P},mathbb{Q})simeqmathsf{Pois}_n^c$ in rational cohomology (and an analogue of our extra involution requirement in the case $4mid n$) is rationally weakly equivalent to an operad in simplicial sets $LG_{bullet}(mathsf{Pois}_n^c)$ which we determine from the $n$-Poisson cooperad $mathsf{Pois}_n^c$. We also prove that the morphisms $iota: mathsf{D}_mrightarrowmathsf{D}_n$, which link the little discs operads together, are rationally formal as soon as $n-mgeq 2$. These results enable us to retrieve the (real) formality theorems of Kontsevich by a new approach, and to sort out the question of the existence of formality quasi-isomorphisms defined over the rationals (and not only over the reals) in the case of the little discs operads of dimension $ngeq 3$." @default.
- W4300190312 created "2022-10-03" @default.
- W4300190312 creator A5005254307 @default.
- W4300190312 creator A5017888005 @default.
- W4300190312 date "2015-03-30" @default.
- W4300190312 modified "2023-09-28" @default.
- W4300190312 title "The intrinsic formality of $E_n$-operads" @default.
- W4300190312 doi "https://doi.org/10.48550/arxiv.1503.08699" @default.
- W4300190312 hasPublicationYear "2015" @default.
- W4300190312 type Work @default.
- W4300190312 citedByCount "0" @default.
- W4300190312 crossrefType "posted-content" @default.
- W4300190312 hasAuthorship W4300190312A5005254307 @default.
- W4300190312 hasAuthorship W4300190312A5017888005 @default.
- W4300190312 hasBestOaLocation W43001903121 @default.
- W4300190312 hasConcept C114614502 @default.
- W4300190312 hasConcept C115624301 @default.
- W4300190312 hasConcept C138885662 @default.
- W4300190312 hasConcept C185592680 @default.
- W4300190312 hasConcept C202444582 @default.
- W4300190312 hasConcept C203436722 @default.
- W4300190312 hasConcept C2777159308 @default.
- W4300190312 hasConcept C33923547 @default.
- W4300190312 hasConcept C41895202 @default.
- W4300190312 hasConcept C5961521 @default.
- W4300190312 hasConcept C78606066 @default.
- W4300190312 hasConcept C8010536 @default.
- W4300190312 hasConceptScore W4300190312C114614502 @default.
- W4300190312 hasConceptScore W4300190312C115624301 @default.
- W4300190312 hasConceptScore W4300190312C138885662 @default.
- W4300190312 hasConceptScore W4300190312C185592680 @default.
- W4300190312 hasConceptScore W4300190312C202444582 @default.
- W4300190312 hasConceptScore W4300190312C203436722 @default.
- W4300190312 hasConceptScore W4300190312C2777159308 @default.
- W4300190312 hasConceptScore W4300190312C33923547 @default.
- W4300190312 hasConceptScore W4300190312C41895202 @default.
- W4300190312 hasConceptScore W4300190312C5961521 @default.
- W4300190312 hasConceptScore W4300190312C78606066 @default.
- W4300190312 hasConceptScore W4300190312C8010536 @default.
- W4300190312 hasLocation W43001903121 @default.
- W4300190312 hasLocation W43001903122 @default.
- W4300190312 hasLocation W43001903123 @default.
- W4300190312 hasOpenAccess W4300190312 @default.
- W4300190312 hasPrimaryLocation W43001903121 @default.
- W4300190312 hasRelatedWork W1886936913 @default.
- W4300190312 hasRelatedWork W1972112806 @default.
- W4300190312 hasRelatedWork W2056663089 @default.
- W4300190312 hasRelatedWork W2572227777 @default.
- W4300190312 hasRelatedWork W2832047942 @default.
- W4300190312 hasRelatedWork W2963057596 @default.
- W4300190312 hasRelatedWork W2964209987 @default.
- W4300190312 hasRelatedWork W2990587355 @default.
- W4300190312 hasRelatedWork W3138876552 @default.
- W4300190312 hasRelatedWork W4288020953 @default.
- W4300190312 isParatext "false" @default.
- W4300190312 isRetracted "false" @default.
- W4300190312 workType "article" @default.