39 citations · 156 across the 12 of their papers we have counts for
12 papers
Dg manifolds, formal exponential maps and homotopy Lie algebras
Seokbong Seol, Mathieu Stiénon, Ping Xu
This paper is devoted to the study of the relation between `formal exponential maps,' the Atiyah class, and Kapranov algebras associated with dg manifolds in the $C^\…
Polyvector fields and polydifferential operators associated with Lie pairs
Ruggero Bandiera, Mathieu Stiénon, Ping Xu
We prove that the spaces and $\operatorname{tot}\big(Γ(Λ^\bullet A^\vee)\otime…
Formality for g-manifolds
Hsuan-Yi Liao, Mathieu Stiénon, Ping Xu
To any -manifold are associated two dglas and $\ope…
Formality and Kontsevich--Duflo type theorems for Lie pairs
Hsuan-Yi Liao, Mathieu Stiénon, Ping Xu
$\newcommand{\poly}{_{\operatorname{poly}}^{\bullet}}\newcommand{\td}{(\operatorname{td}_{L/A}^{\nabla})^{\frac{1}{2}}}\newcommand{\cx}[1]{\operatorname{tot}\big(Γ(Λ^\bullet A^\vee…
Fedosov dg manifolds associated with Lie pairs
Mathieu Stiénon, Ping Xu
Given any pair of Lie algebroids, we construct a differential graded manifold , which we call Fedosov dg manifold. We prove that the cohomological vecto…
Formal exponential map for graded manifolds
Hsuan-Yi Liao, Mathieu Stiénon
We introduce, for every -graded manifold, a formal exponential map defined in a purely algebraic way and study its properties. As an application, we give a simple new c…
The Atiyah class of a dg-vector bundle
Rajan Amit Mehta, Mathieu Stiénon, Ping Xu
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 vecto…
A Hopf algebra associated to a Lie pair
Zhuo Chen, Mathieu Stiénon, Ping Xu
The quotient of a pair of Lie algebroids is a Lie algebra object in the derived category of the category of left $\m…
Poincaré--Birkhoff--Witt isomorphisms and Kapranov dg-manifolds
Camille Laurent-Gengoux, Mathieu Stiénon, Ping Xu
We prove that to every inclusion of Lie algebroids over the same base manifold corresponds a Kapranov dg-manifold structure on , which is c…
From Hypercomplex to Holomorphic Symplectic Structures
Wei Hong, Mathieu Stiénon
The notions of holomorphic symplectic structures and hypercomplex structures on Courant algebroids are introduced and then proved to be equivalent. These generalize hypercomplex tr…
Exponential map and algebra associated to a Lie pair
Camille Laurent-Gengoux, Mathieu Stiénon, Ping Xu
In this note, we unveil homotopy-rich algebraic structures generated by the Atiyah classes relative to a Lie pair of algebroids. In particular, we prove that the quotient $…
Matched pairs of Courant algebroids
Melchior Grützmann, Mathieu Stiénon
We introduce the notion of matched pairs of Courant algebroids and give several examples arising naturally from complex manifolds, holomorphic Courant algebroids, and certain regul…