TY - JOUR

T1 - Hochschild Cohomology of dg Manifolds Associated to Integrable Distributions

AU - Chen, Zhuo

AU - Xiang, Maosong

AU - Xu, Ping

N1 - 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.

UR - http://www.scopus.com/inward/record.url?scp=85137868566&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85137868566&partnerID=8YFLogxK

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 -