Atiyah and Todd classes arising from integrable distributions

Zhuo Chen, Maosong Xiang, Ping Xu

Research output: Contribution to journalArticle

Abstract

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].

LanguageEnglish (US)
Pages52-67
Number of pages16
JournalJournal of Geometry and Physics
Volume136
DOIs
StatePublished - Feb 1 2019

Fingerprint

Lie Algebroids
Michael Francis Atiyah
Foliation
Isomorphic
Complex Manifolds
Kähler Manifold
Class
Compact Manifold

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Cite this

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Atiyah and Todd classes arising from integrable distributions. / Chen, Zhuo; Xiang, Maosong; Xu, Ping.

In: Journal of Geometry and Physics, Vol. 136, 01.02.2019, p. 52-67.

Research output: Contribution to journalArticle

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