Atiyah and Todd classes arising from integrable distributions

Zhuo Chen, Maosong Xiang, Ping Xu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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].

Original languageEnglish (US)
Pages (from-to)52-67
Number of pages16
JournalJournal of Geometry and Physics
Volume136
DOIs
StatePublished - Feb 2019

All Science Journal Classification (ASJC) codes

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

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