Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606052 | Differential Geometry and its Applications | 2013 | 9 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Christine Jost,