TY - JOUR

T1 - Hochschild Cohomology of dg Manifolds Associated to Integrable Distributions

AU - Chen, Zhuo

AU - Xiang, Maosong

AU - Xu, Ping

N1 - Funding Information:
Research partially supported by NSFC grant 12071241 (Chen), NSFC grant 11901221 (Xiang), and NSF grants DMS-1707545 and DMS-2001599 (Xu).
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022/12

Y1 - 2022/12

N2 - For the field K= R or C, and an integrable distribution F⊆ TM⊗ RK 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.

AB - For the field K= R or C, and an integrable distribution F⊆ TM⊗ RK 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.

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U2 - 10.1007/s00220-022-04473-z

DO - 10.1007/s00220-022-04473-z

M3 - Article

AN - SCOPUS:85137868566

SN - 0010-3616

VL - 396

SP - 647

EP - 684

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -