Atiyah and Todd classes of regular Lie algebroids

Abstract

For any regular Lie algebroid $A$, the kernel $K$ and the image $F$ of its anchor map ${\rho }_A$, together with $A$ itself fit into a short exact sequence, called Atiyah sequence, of Lie algebroids. We prove that Atiyah and Todd classes of dg manifolds arising from regular Lie algebroids respect the Atiyah sequence. That is, the Atiyah and Todd classes of $A$ restrict to the Atiyah and Todd classes of the bundle $K$ of Lie algebras on the one hand, and project onto the Atiyah and Todd classes of the integrable distribution $F\subseteq T_M$ on the other hand.

22 pages. This manuscript has been accepted for publication in SCIENCE CHINA Mathematics

References in corpus (2)

• The Atiyah class of a dg-vector bundle
• Atiyah and Todd classes arising from integrable distributions