OA Seminar by Ryszard Nest, UCPH

L_\infty-algebras, two groupoids and deformation quantization of gerbes.

Abstract:

Extension of the M. Kontsevich formality theorem to gerbes necessitates extension of the notion of Deligne 2-groupoid to L∞ algebras. For a differential graded Lie algebra g which is zero below the degree －1, the nerve of the Deligne 2-groupoid is homotopy equivalent to the Hinich simplicial set of g-valued differential forms. This allowes a formulation of the formality theorem in the presence of a grebe on the manifold in question. We will explain the notions involved in this result and sketch the application to the formality theorem.