Abstract
The constructions appearing in the formality theorem by Kontsevich [9] and Tamarkin [13] are first made locally. In these references, sufficient conditions are given to globalize the formality maps. Kontsevich formality maps satisfy these conditions. In this Letter, we show that Tamarkin’s maps can also be constructed so as to satify these conditions, thus can be globalized.
Similar content being viewed by others
References
F Bayen M Flato C Fronsdal A Lichnerowicz D Sternheimer (1975/1977) ArticleTitleQuantum mechanics as a deformation of classical mechanics Lett. Math. Phys. 1 IssueID6 521–530
F. Bayen M. Flato C. Fronsdal A. Lichnerowicz D. Sternheimer (1977) ArticleTitleDeformation theory and quantization, I and II Ann. Phys. 111 61–151
Dolgushev, V.: Covariant and equivariant formality theorems, math.QA/0307212.
G. Ginot (2004) ArticleTitleAnn. Math. Blaise Pascal Homologie et modèle minimal des algèbres de Gerstenhaber 11 IssueID1 95–127
G. Ginot G. Halbout (2003) ArticleTitleA formality theorem for Poisson manifold Lett. Math. Phys. 66 IssueID1-2 37–64
V. Ginzburg M. Kapranov (1994) ArticleTitleKoszul duality for operads Duke Math. J. 76 IssueID1 203–272
G. Halbout (2001) ArticleTitleFormule d’homotopie entre les complexes de Hochschild et de de Rham Compositio Math. 126 IssueID2 123–145
G. Hochschild B. Kostant A. Rosenberg (1962) ArticleTitleDifferential forms on regular affine algebras Trans. AMS 102 383–408
M. Kontsevich (2003) ArticleTitleDeformation quantization of Poisson manifolds Lett. Math. Phys. 66 IssueID3 157–216
M. Kontsevich Y. Soibelman (2000) ArticleTitleMath. Phys. Stud. Deformations of algebras over operads and the Deligne conjecture, Conférence Moshé Flato 1999, Vol. I (Dijon) 21 255–307
Koszul, J. L.: Crochet de Schouten-Nijenjuis et cohomologie in ‘‘Elie Cartan et les mathémati-ques d’aujourd’hui’’, Astérisque (1985), 257–271.
T. Lada J. D. Stasheff (1993) ArticleTitleIntroduction to SH Lie algebras for physicists Int. J. Theoret. Phys. 32 IssueID7 1087–1103
Tamarkin, D.: Another proof of M. Kontsevich’s formality theorem, math.QA/9803025.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Halbout, G. Globalization of Tamarkin’s Formality Theorem. Lett Math Phys 71, 39–48 (2005). https://doi.org/10.1007/s11005-004-5926-3
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11005-004-5926-3