The Atiyah class of a dg-vector bundle

Rajan Amit Mehta, Mathieu Stiénon, Ping Xu

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We introduce the notions of Atiyah class and Todd class of a differential graded vector bundle with respect to a differential graded Lie algebroid. We prove that the space of vector fields X(M) on a dg-manifold M with homological vector field Q admits a structure of L[1]-algebra with the Lie derivative LQ as unary bracket λ1, and the Atiyah cocycle AtM corresponding to a torsion-free affine connection as binary bracket λ2.

Original languageEnglish (US)
Pages (from-to)357-362
Number of pages6
JournalComptes Rendus Mathematique
Volume353
Issue number4
DOIs
StatePublished - Apr 1 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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