Isaac Newton Institute for Mathematical Sciences

Kontsevich's graph complex, GRT, and the deformation complex of the sheaf of polyvector fields

Presenter: Christopher L. Rogers (University of Göttingen)

Co-authors: Vasily Dolgushev (Temple University), Thomas Willwacher (Harvard University)

Abstract

Here I present recent joint work (arXiv:1211.4230) with V. Dolgushev and T. Willwacher. In this work, we generalize Kontsevich's construction of L-infinity derivations of polyvector fields from affine space to an arbitrary smooth algebraic variety. More precisely, we construct a map (in the homotopy category) from Kontsevich's graph complex to the deformation complex of the sheaf of polyvector fields on a smooth algebraic variety. Using this we show that the action of the Deligne-Drinfeld elements of the Grothendieck-Teichmüller Lie algebra on the cohomology of the sheaf of polyvector fields coincides with the action of odd components of the Chern character.