Title A proof of the Tsygan formality conjecture for chains Author Shoikhet, Boris Faculty/Department Faculty of Sciences. Mathematics and Computer Science Publication type article Publication 2003 New York, N.Y. , 2003 Subject Mathematics Source (journal) Advances in mathematics. - New York, N.Y. Volume/pages 179(2003) :1 , p. 7-37 ISSN 0001-8708 ISI 000185640500002 Carrier E Target language English (eng) Full text (Publishers DOI) Abstract We extend the Kontsevich formality L∞-morphism to an L∞-morphism of L∞-modules over . The construction of the map is given in Kontsevich-type integrals. The conjecture that such an L∞-morphism exists is due to Boris Tsygan (Formality Conjecture for Chains, math. QA/9904132). As an application, we obtain an explicit formula for isomorphism is the Kontsevich deformation quantization of the algebra A by a Poisson bivector field, and {,} is the Poisson bracket). We also formulate a conjecture extending the Kontsevich theorem on cup-products to this context. The conjecture implies a generalization of the Duflo formula, and many other things. E-info https://repository.uantwerpen.be/docman/iruaauth/1c7d4a/651e26a307d.pdf http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000185640500002&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000185640500002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000185640500002&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848