Department: Department of Mathematics            PI's Name: Hsuan-Yi Liao

Journal: Communications in Mathematical Physics

Title: Atiyah Classes and Todd Classes of Pullback dg Lie Algebroids Associated with Lie Pairs

Abstract: For a Lie algebroid L → M and a Lie subalgebroid A → M, i.e. a Lie pair (L, A), we study the Atiyah class and the Todd class of the pullback dg (i.e. differential graded) Lie algebroid of L along the bundle projection p:A[1] → M of the shifted vector bundle A[1]. Applying the homological perturbation lemma, we provide a new construction of Stiénon–Vitagliano–Xu’s contraction. Using this contraction, we construct two special isomorphisms. We prove that this pair of isomorphisms identifies the Atiyah class and the Todd class of the dg Lie algebroid p^!L with the Atiyah class and the Todd class of the Lie pair (L, A), respectively.