Logarithms and deformation quantization

• 成果类型: Article
• 署名作者: Alekseev, Anton; Rossi, Carlo A.; Torossian, Charles; Willwacher, Thomas
• 署名单位: University of Geneva; Universite Paris Cite; University of Zurich
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0647-7
• 发表日期: 2016
• 页码: 1-28
• 关键词: equivalence

摘要

We prove the statement/conjecture of M. Kontsevich on the existence of the logarithmic formality morphism . This question was open since 1999, and the main obstacle was the presence of dr / r type singularities near the boundary in the integrals over compactified configuration spaces. The novelty of our approach is the use of local torus actions on configuration spaces of points in the upper half-plane. It gives rise to a version of Stokes' formula for differential forms with singularities at the boundary which implies the formality property of . We also show that the logarithmic formality morphism admits a globalization from to an arbitrary smooth manifold.