The minimal model of the Batalin-Vilkovisky operad
Abstract: The purpose of this talk is to explain and to generalize, in a homotopical way, the result of Barannikov-Kontsevich and Manin which states that the underlying homology groups of some Batalin-Vilkovisky algebras carry a Frobenius manifold structure. To this extent, we first make the minimal model for the operad encoding BV-algebras explicit. Then we extend the action of the homology of the Deligne-Mumford moduli space of genus $0$ curves on the homology of some BV-algebras to an action via higher homotopical operations organized by the cohomology of the open moduli space of genus zero curves. Applications in Poisson geometry and Lie algebra cohomology and to the Mirror Symmetry conjecture will be given. [Based on the joint paper ArXiv:1105.2008 with Gabriel Drummond-Cole.]
Speaker : Bruno Vallette (Université de Nice Sophia-Antipolis).