| ABSTRACT |
In the formulation of his celebrated Formality conjecture, M. Kontsevich introduced a universal version of the deformation theory for the Schouten algebra of polyvector fields on affine manifolds. This construction is reviewed and generalised to graded symplectic manifolds of arbitrary degree n ≥ 1. The corresponding graph model is given by the full Kontsevich graph complex fGCd where d=n+1 stands for the dimension of the associated AKSZ type σ-model. This generalisation is instrumental to classify universal structures on graded symplectic manifolds. We conclude by discussing the possible role played by this new deformation theory regarding the quantization problem for Courant algebroids and higher symplectic Lie-n algebroids. |
