Globalizing L∞L∞-automorphisms of the Schouten algebra of polyvector fields

Recently, Willwacher showed that the Grothendieck–Teichmüller group GRT acts by L∞L∞-automorphisms on the Schouten algebra of polyvector fields Tpoly(Rd)Tpoly(Rd) on affine space RdRd. In this article, we prove that a large class of L∞L∞-automorphisms on Tpoly(Rd)Tpoly(Rd), including Willwacherʼs, can be globalized. That is, given an L∞L∞-automorphism of Tpoly(Rd)Tpoly(Rd) and a general smooth manifold M   with the choice of a torsion-free connection, we give an explicit construction of an L∞L∞-automorphism of the Schouten algebra Tpoly(M)Tpoly(M) on the manifold M, depending on the chosen connection. The method we use is the Fedosov trick.