The Atiyah Class of a dg-Vector Bundle

Authors

Rajan Amit Mehta, Smith CollegeFollow
Mathieu Stiénon, The Pennsylvania State University
Ping Xu, The Pennsylvania State University

Document Type

Article

Publication Date

4-2015

Publication Title

Comptes Rendus Mathematique

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 λ₁, and the Atiyah cocycle At_M corresponding to a torsion-free affine connection as binary bracket λ₂.

Volume

353

Issue

4

First Page

357

Last Page

362

DOI

dx.doi.org/10.1016/j.crma.2015.01.019

ISSN

1631-073X

Comments

Peer reviewed accepted manuscript.

En hommage à Charles-Michel Marle à l’occasion de son quatre-vingtième anniversaire.

Recommended Citation

Mehta, Rajan Amit; Stiénon, Mathieu; and Xu, Ping, "The Atiyah Class of a dg-Vector Bundle" (2015). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/16