TY - JOUR
T1 - Atiyah and Todd classes arising from integrable distributions
AU - Chen, Zhuo
AU - Xiang, Maosong
AU - Xu, Ping
N1 - Funding Information:
Xiang is grateful to his advisor Xiaobo Liu for his constant support and encouragement, to Pennsylvania State University, United States for its hospitality and to China Scholarship Council for the financial support during his 20-months stay at Penn State. We are grateful to Ruggero Bandiera for bringing us attention to Ref. [10] on the tensor product of homotopy contractions. We also wish to thank Damien Broka, Hsuan-Yi Liao and Mathieu Stiénon for helpful discussions.
Funding Information:
Chen’sresearch was partially supported by National Natural Science Foundation of China (NSFC), China grant 11471149 . Xu’s research was partially supported by National Science Foundation (NSF), United States grants DMS-1406668 and DMS-1707545 .
Funding Information:
Chen'sresearch was partially supported by National Natural Science Foundation of China (NSFC), China grant 11471149. Xu's research was partially supported by National Science Foundation (NSF), United States grants DMS-1406668 and DMS-1707545.
Publisher Copyright:
© 2018
PY - 2019/2
Y1 - 2019/2
N2 - In this paper, we study the Atiyah class and the Todd class of the DG manifold [Formula presented] corresponding to an integrable distribution [Formula presented], where [Formula presented] or ℂ. We show that these two classes are canonically identical to those of the Lie pair [Formula presented]. As a consequence, the Atiyah class of a complex manifold X is isomorphic to the Atiyah class of the corresponding DG manifold [Formula presented]. Moreover, if X is a compact Kähler manifold, then the Todd class of X is also isomorphic to the Todd class of the corresponding DG manifold [Formula presented].
AB - In this paper, we study the Atiyah class and the Todd class of the DG manifold [Formula presented] corresponding to an integrable distribution [Formula presented], where [Formula presented] or ℂ. We show that these two classes are canonically identical to those of the Lie pair [Formula presented]. As a consequence, the Atiyah class of a complex manifold X is isomorphic to the Atiyah class of the corresponding DG manifold [Formula presented]. Moreover, if X is a compact Kähler manifold, then the Todd class of X is also isomorphic to the Todd class of the corresponding DG manifold [Formula presented].
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U2 - 10.1016/j.geomphys.2018.10.011
DO - 10.1016/j.geomphys.2018.10.011
M3 - Article
AN - SCOPUS:85056642826
SN - 0393-0440
VL - 136
SP - 52
EP - 67
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
ER -