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arXiv · 1502.03119

The Atiyah class of a dg-vector bundle

Rajan Amit Mehta·Mathieu Stiénon·Ping Xu
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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 on a dg-manifold with homological vector field $Q$ admits a structure of L-infinity algebra with the Lie derivative $L_Q$ as unary bracket, and the Atiyah cocycle corresponding to a torsion-free affine connection as binary bracket.

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Rajan Amit Mehta, Mathieu Stiénon, Ping Xu. 2015-02-10. The Atiyah class of a dg-vector bundle. https://doi.org/10.1016/j.crma.2015.01.019

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