2003/04/01 by Grégory Ginot, Ginot, Grégory, Gilles Halbout +1
Mathematics · #16S80 #53D55 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 16E40 #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Secondary 18D50 #math.DG #math.QA #math.RA #msc:16E40 #msc:16S80 #msc:18D50 #msc:53D55
paper · pdf · doi:10.48550/arxiv.math/0304004
10 pages, case of $C\_\infty$-morphisms is studied, existence of lift is proved in that case, final version, to appear in Proc. of the A.M.S
arxiv created 2005/06/29 · arxiv updated 2016/08/16
Let \g_2 be the Hochschild complex of cochains on C^∞(\RMn) and \g_1 be the space of multivector fields on \RMn. In this paper we prove that given any G_∞-structure (\rm i.e. Gerstenhaber algebra up to homotopy structure) on \g_2, and any C_∞-morphism ϕ (\rm i.e. morphism of commutative, associative algebra up to homotopy) between \g_1 and \g_2, there exists a G_∞-morphism Φ between \g_1 and \g_2 that restricts to ϕ. We also show that any L_∞-morphism (\rm i.e. morphism of Lie algebra up to homotopy), in particular the one constructed by Kontsevich, can be deformed into a G_∞-morphism, using Tamarkin's method for any G_∞-structure on \g_2. We also show that any two of such G_∞-morphisms are homotopic.