For any regular Lie algebroid A, the kernel K and the image F of its anchor map ρA, together with A itself fit into a short exact sequence, called the Atiyah sequence, of Lie algebroids. We prove that the Atiyah and ...For any regular Lie algebroid A, the kernel K and the image F of its anchor map ρA, together with A itself fit into a short exact sequence, called the Atiyah sequence, of Lie algebroids. We prove that the Atiyah and Todd classes of dg manifolds arising from a regular Lie algebroid respect the Atiyah sequence, i.e.,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■T_M on the other hand.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11901221)。
文摘For any regular Lie algebroid A, the kernel K and the image F of its anchor map ρA, together with A itself fit into a short exact sequence, called the Atiyah sequence, of Lie algebroids. We prove that the Atiyah and Todd classes of dg manifolds arising from a regular Lie algebroid respect the Atiyah sequence, i.e.,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■T_M on the other hand.
