Proof of swiss cheese version of deligne's conjecture

V. A. Dolgushev; D. E. Tamarkin; B. L. Tsygan

doi:10.1093/imrn/rnq265

Proof of swiss cheese version of deligne's conjecture

V. A. Dolgushev, D. E. Tamarkin^*, B. L. Tsygan

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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.].

Original language	English (US)
Pages (from-to)	4666-4746
Number of pages	81
Journal	International Mathematics Research Notices
Volume	2011
Issue number	20
DOIs	https://doi.org/10.1093/imrn/rnq265
State	Published - 2011

Funding

D.T. and B.T. are supported by NSF grants. This work is supported by the NSF grant DMS 0856196 (to V.D.) and Regent’s Faculty Fellowship, and the Grant for Support of Scientific Schools NSh-8065.2006.2.

ASJC Scopus subject areas

General Mathematics

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AU - Tamarkin, D. E.

AU - Tsygan, B. L.

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N2 - 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.].

AB - 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.].

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Proof of swiss cheese version of deligne's conjecture

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