The Atiyah class of a dg-vector bundle

By R. Mehta, Mathieu Sti'enon, P. Xu. 2015

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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 X ( M ) on a dg-manifold M with homological vector field Q admits a structure of L ∞ [ 1 ] -algebra with the Lie derivative L Q as unary bracket λ 1 , and the Atiyah cocycle At M corresponding to a torsion-free affine connection as binary bracket λ 2 .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/14961dfc1723caf7192a9ed0b5951f557971ac7d