EVENT DETAILS AND ABSTRACT

Title: Deformation theory of representations of prop(erad)s
Speaker: Bruno Vallette
Speaker Info: University of Nice
Brief Description:
Special Note:
Abstract:

To any morphism of prop(erad)s, we define a chain complex, à la Quillen, which mesures its deformations. In this way, we give a conceptual explanation of well known cohomology theories (Hochschild, Harrison, Chevalley-Eilenberg, Gerstenhaber-Schack). We will show that this chain complex has a rich algebraic structure, generalizing some operations (braces) involved in the proof of Deligne's conjecture. As a corollary, we get a Lie bracket (up to homotopy) on this deformation complex whose Maurer-Cartan elements will be studied. For instance, structures of (bial)gebra up to homotopy over a prop(erad) will be interpreted in this way. [Joint work with Sergei Merkulov]