Derived Grothendieck-Teichmüller group and graphcomplexes, after T. Willwacher
Also appears in collection : Bourbaki - 14 janvier 2017
Graph complex is spanned by equivalence classes of finite connected graphs with thedual differential given by the sum of all contractions of edges, with appropriate signs. This complex forms a differential graded Lie algebra, and acts as a universal derived infinitesimalsymmetry of all graded Lie algebras of polyvector fields on finite-dimensional manifolds. Grothendieck-Teichmüller group, as defined by V. Drinfeld, is the group of symmetries of thetower of rationally completed braid groups. Recent breakthrough by T. Willwacher identifiesthe graph complex with the derived version of GT group. This result settles essentially all openquestions in the subject of deformation quantization and little disc operads.