{"paper":{"title":"The intrinsic formality of $E_n$-operads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Benoit Fresse, Thomas Willwacher","submitted_at":"2015-03-30T15:02:44Z","abstract_excerpt":"We establish that $E_n$-operads satisfy a rational intrinsic formality theorem for $n\\geq 3$. 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 $n\\geq 3$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08699","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}