A celebrated theorem of Kapranov states that the Atiyah class of the tangent bundle of a
complex manifold X makes TX− 1 into a Lie algebra object in D+(X), the bounded below …

The Atiyah–Singer index theorem and the mathematics around it–the theory of elliptic and
pseudodifferential operators, K–theory, cobordism, and so on–has a long-standing …

This paper is devoted to the study of the relation between 'formal exponential maps,'the
Atiyah class, and Kapranov L∞[1] algebras associated with dg manifolds in the C∞ context …

Abstract Ideas of Rozansky and Witten, as developed by Kapranov, show that a complex
symplectic manifold X gives rise to Vassiliev weight systems. In this paper we study these …

We prove that to every inclusion A↪ L of Lie algebroids over the same base manifold M
corresponds a Kapranov dg-manifold structure on A [1]⊕ L/A, which is canonical up to …

This write up attempts to clarify a preprint by Markarian [2] which proves This paper attempts
to clarify a preprint of Markarian [2]. The preprint by Markarian [2] proves the relative …

In this expository paper, we survey some recent works on the Atiyah class and other
characteristic classes of dg manifolds. In particular, we describe a Kontsevich–Duflo type …

For the field K= R or C, and an integrable distribution F⊆ TM⊗ RK on a smooth manifold M,
we study the Hochschild cohomology of the dg manifold (F [1], d F) and establish a …

We introduce symplectic structures on “Lie pairs” of (real or complex) Lie algebroids as
studied by Chen et al.(From Atiyah classes to homotopy Leibniz algebras. arXiv: 1204.1075 …

We apply the technique of S^ 1-equivariant localization to sheaves on loop spaces in
derived algebraic geometry, and obtain a fundamental link between two families of …