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

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

2008-07-31

arxiv.org/abs/0807.5117v1

Mathematics

K-Theory and Homology

To Mikhail Olshanetsky on the occasion of his 70th birthday

Scientific paper

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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