Hochschild Cohomology of dg Manifolds Associated to Integrable Distributions

Zhuo Chen, Maosong Xiang, Ping Xu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


For the field K= R or C, and an integrable distribution F⊆ TMRK on a smooth manifold M, we study the Hochschild cohomology of the dg manifold (F[1] , dF) and establish a canonical isomorphism with the Hochschild cohomology of the algebra of functions on leaf space in terms of transversal polydifferential operators of F. In particular, for the dg manifold (TX0,1[1],∂¯) associated with a complex manifold X, we prove that its Hochschild cohomology is canonically isomorphic to the Hochschild cohomology HH∙(X) of the complex manifold X. As an application, we show that the Duflo-Kontsevich type theorem for the dg manifold (TX0,1[1],∂¯) implies the Duflo-Kontsevich theorem for complex manifolds.

Original languageEnglish (US)
Pages (from-to)647-684
Number of pages38
JournalCommunications In Mathematical Physics
Issue number2
StatePublished - Dec 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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