Proof of Swiss Cheese Version of Deligne's Conjecture

Proof of Swiss Cheese Version of Deligne's Conjecture

For an associative algebra A, we consider the pair "the Hochschild cochain complex C *(A,A) and the algebra A". There is a natural 2-colored operad which acts on this pair. We show that this operad is quasi-isomorphic to the singular chain operad of Voronov's Swiss Cheese operad. This...

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Veröffentlicht in:International mathematics research notices 2011-01, Vol.2011 (20), p.4666-4746
Hauptverfasser: Dolgushev, V. A., Tamarkin, D. E., Tsygan, B. L.
Format: Artikel
Sprache:eng
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Zusammenfassung:For an associative algebra A, we consider the pair "the Hochschild cochain complex C *(A,A) and the algebra A". There is a natural 2-colored operad which acts on this pair. We show that this operad is quasi-isomorphic to the singular chain operad of Voronov's Swiss Cheese operad. This statement is the Swiss Cheese version of the Deligne conjecture formulated by M. Kontsevich ["Operads and motives in deformation quantization." Letters in Mathematical Physics 48 (1999) 35-72.].
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnq265