13 citations · 45 across the 12 of their papers we have counts for
12 papers
Duflo--Kontsevich-type isomorphisms for Tamarkin--Tsygan calculi of dg manifolds
Hsuan-Yi Liao, Mathieu Stiénon, Ping Xu
We establish a Duflo--Kontsevich-type theorem for differential graded (dg) manifolds. Specifically, we prove that the Hochschild--Kostant--Rosenberg maps twisted by the square root…
Formal geometry and Tamarkin--Tsygan calculi of dg manifolds
Hsuan-Yi Liao, Mathieu Stiénon, Ping Xu
The main goal of this paper is to study the formal geometry of dg manifolds à la Fedosov. For any dg manifold , we construct a Fedosov dg foliation (or dg Lie alg…
Vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair
Hua-Shin Chang, Hsuan-Yi Liao
We investigate vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair , i.e. a pair of a Lie algebroid and a Lie subalgebroid of . The construct…
Differential graded manifolds of finite positive amplitude
Kai Behrend, Hsuan-Yi Liao, Ping Xu
We prove that dg manifolds of finite positive amplitude, i.e. bundles of positively graded curved -algebras, form a category of fibrant objects. As a main step in the…
On the structure of étale fibrations of -bundles
Kai Behrend, Hsuan-Yi Liao, Ping Xu
We prove that an étale fibration between -bundles admits local sections composed of several elementary morphisms of particularly simple and accessible type. As applicatio…
Atiyah classes and Todd classes of pullback dg Lie algebroids associated with Lie pairs
Hsuan-Yi Liao
For a Lie algebroid and a Lie subalgebroid , i.e. a Lie pair , we study the Atiyah class and the Todd class of the pullback dg (i.e. differential graded) Lie algebroi…
Keller admissible triples and Duflo theorem
Hsuan-Yi Liao, Seokbong Seol
The present paper is devoted to the study of Keller admissible triples. We prove that a Keller admissible triple induces an isomorphism of Gerstenhaber algebras between the Hochsch…
Derived Differentiable Manifolds
Kai Behrend, Hsuan-Yi Liao, Ping Xu
We develop the theory of derived differential geometry in terms of bundles of curved -algebras, i.e. dg manifolds of positive amplitudes. We prove the category of deri…
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…
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…
Semi-topological Galois theory and the inverse Galois problem
Hsuan-Yi Liao, Jyh-Haur Teh
We enhance the analogy between field extensions and covering spaces by introducing the concept of splitting covering which correspondences to the splitting field in Galois theory.…