GT seminar: "The Fedosov product on differential forms and flat connections on differential graded manifolds"

Abstract: The Hochschild-Kostant-Rosenberg theorem relates negative cyclic homology of the functions on a differential graded manifold M to the de Rham complex of M. The natural A-infinity structure on negative cyclic homology corresponds to an A-infinity structure on the de Rham complex called the Fedosov product. (This product agrees with the usual one if either argument is closed, but it is not graded symmetric in general.) In this talk, we study the analogue of flat connections for this product: these are in bijection with flat connections for the usual product on the classical locus but appear to be different in general. The non-commutative analogue of the Gauss-Manin connection is our main example.

This is a talk in our geometry and topology seminar series.