Globalizing L-infinity automorphisms of the Schouten algebra of polyvector fields
(English)In: Differential geometry and its applications (Print), ISSN 0926-2245Article in journal (Refereed) Accepted
Recently, Willwacher showed that the Grothendieck-Teichmuller group GRT acts by L-infinity-automorphisms on the Schouten algebra of polyvector fields T_poly(R^d) on affine space R^d. In this article, we prove that a large class of L-infinity-automorphisms on the Schouten algebra, including Willwacher's, can be globalized. That is, given an L-infinity-automorphism of T_poly(R^d) and a general smooth manifold M with the choice of a torsion-free connection, we give an explicit construction of an L-infinity-automorphism of the Schouten algebra T_poly(M) on the manifold M, depending on the chosen connection. The method we use is the Fedosov trick.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-87356OAI: oai:DiVA.org:su-87356DiVA: diva2:602958