{"paper":{"title":"The rational homology of spaces of long knots in codimension >2","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Ismar Volic, Pascal Lambrechts, Victor Tourtchine","submitted_at":"2007-03-21T20:14:07Z","abstract_excerpt":"We determine the rational homology of the space of long knots in R^d for $d\\geq4$. Our main result is that the Vassiliev spectral sequence computing this rational homology collapses at the E^1 page. As a corollary we get that the homology of long knots (modulo immersions) is the Hochschild homology of the Poisson algebras operad with a bracket of degree d-1, which can be obtained as the homology of an explicit graph complex and is in theory completely computable.\n  Our proof is a combination of a relative version of Kontsevich's formality of the little d-disks operad and of Sinha's cosimplicia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703649","kind":"arxiv","version":1},"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"}