{"paper":{"title":"A proof of the Tsygan formality conjecture for chains","license":"","headline":"","cross_cats":["hep-th","math.AC","math.KT"],"primary_cat":"math.QA","authors_text":"Boris Shoikhet (ETH-Zentrum & IPDE)","submitted_at":"2000-10-31T18:51:45Z","abstract_excerpt":"We extend the Kontsevich formality $L_\\infty$-morphism $\\U\\colon T^\\ndot_\\poly(\\R^d)\\to\\D^\\ndot_\\poly(\\R^d)$ to an $L_\\infty$-morphism of an $L_\\infty$-modules over $T^\\ndot_\\poly(\\R^d)$, $\\hat \\U\\colon C_\\ndot(A,A)\\to\\Omega^\\ndot(\\R^d)$, $A=C^\\infty(\\R^d)$. The construction of the map $\\hat \\U$ is given in Kontsevich-type integrals. The conjecture that such an $L_\\infty$-morphism exists is due to Boris Tsygan \\cite{Ts}. As an application, we obtain an explicit formula for isomorphism $A_*/[A_*,A_*]\\simto A/\\{A,A\\}$ ($A_*$ is the Kontsevich deformation quantization of the algebra $A$ by a Pois"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0010321","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0010321/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}