Atiyah and Todd classes of regular Lie algebroids

2021/10/10 by Maosong Xiang, Xiang, Maosong
Mathematics · #53D17 #57R20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2110.04720

openalex publication_date 2021/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any regular Lie algebroid A, the kernel K and the image F of its anchor map ρ_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 ⊆ T_M on the other hand.

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