| GASC Seminar |
| Formality for the homotopy calculus algebra of Hochschild (co)chains |
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Abstract: The standard Cartan calculus on polyvector fields and exterior forms can be naturally extended to the Hochschild cohomology and the Hochschild homology of an arbitrary associative algebra A. Recent results of M. Kontsevich and Y. Soibelman imply that this calculus on Hochschild (co)homology can be naturally upgraded to a homotopy calculus structure on the pair (C•(A), C•(A)) ``Hochschild cochains + Hochschild chains'' of an associative algebra A. In my talk I will consider the sheaf of homotopy calculi (C•(OX), C•(OX)) for a smooth algebraic variety X with OX being the structure sheaf. I will show that this sheaf (C•(OX), C•(OX)) of homotopy calculi is quasi-isomorphic to its cohomology. I will also talk about applications of this result. My talk will be based on joint paper arXiv:0807.5117 with D. Tamarkin and B. Tsygan. The main result of this paper was announced by D. Tamarkin in 2000 at the Moshé Flato memorial conference. |
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Here are some directions to Northeastern University. Lake Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. |
| GASC Seminar Home Page | Posted: August 9, 2008. |
| Web page: Alexandru I. Suciu | URL: http://www.math.neu.edu/gasc/abs/dolgushev08.html |