Atiyah class of DG manifolds of positive amplitude

Abstract

We prove that the Atiyah and Todd classes of differential graded (DG) manifolds of positive amplitude are invariant under the weak equivalences in the sense of Behrend--Liao--Xu. As an application, we show that Hochschild cohomology of the second kind of DG manifolds of positive amplitude is also invariant under weak equivalences as well.

33 pages; minor revisions. To appear in Mathematische Zeitschrift