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arXiv · 0807.5117

Formality of the homotopy calculus algebra of Hochschild (co)chains

Vasiliy Dolgushev·Dmitry Tamarkin·Boris Tsygan
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Abstract

The Kontsevich-Soibelman solution of the cyclic version of Deligne's conjecture and the formality of the operad of little discs on a cylinder provide us with a natural homotopy calculus structure on the pair (C^*(A), C_*(A)) ``Hochschild cochains + Hochschild chains'' of an associative algebra A. We show that for an arbitrary smooth algebraic variety X with the structure sheaf O_X the sheaf (C^*(O_X), C_*(O_X)) of homotopy calculi is formal. This result was announced in paper [29] by the second and the third author.

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Vasiliy Dolgushev, Dmitry Tamarkin, Boris Tsygan. 2008-07-31. Formality of the homotopy calculus algebra of Hochschild (co)chains. https://arxiv.org/abs/0807.5117

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