85 citations · 365 across the 32 of their papers we have counts for
27 papers · 1 filter
Contact resolutions of singular Jacobi structures
Hichem Lassoued, Camille Laurent-Gengoux
We study contact resolutions of Jacobi structures which are contact on an open subset. We give several classes of examples, as well as classes for which it cannot exist.
Normal forms of -graded -manifolds
Alexei Kotov, Camille Laurent-Gengoux, Vladimir Salnikov
Following recent results of A.K. and V.S. on -graded manifolds, we give several local and global normal forms results for -structures on those, i.e. for differential…
Modular class of Lie -algebroids and adjoint representation
Raquel Caseiro, Camille Laurent-Gengoux
We study the modular class of -manifolds, and in particular of negatively graded Lie -algebroid. We show the equivalence of several descriptions of those classes, that i…
On Dirac structures admitting a variational approach
Oscar Cosserat, Camille Laurent-Gengoux, Alexei Kotov +2
We discuss the notion of basic cohomology for Dirac structures and, more generally, Lie algebroids. We then use this notion to characterize the obstruction to a variational formula…
Symplectic resolutions of the quotient of R^2 by a non-finite symplectic group
Hichem Lassoued, Camille Laurent-Gengoux
We construct smooth symplectic resolutions of the quotient of R^2 under some infinite discrete sub-group of GL_2(R) preserving a log-symplectic structure. This extends from algebra…
The neighbourhood of a singular leaf
Camille Laurent-Gengoux, Leonid Ryvkin
An important result for regular foliations is their formal semi-local triviality near simply connected leaves. We extend this result to singular foliations for all 2-connected leav…
The holonomy of a singular leaf
Camille Laurent-Gengoux, Leonid Ryvkin
We introduce the holonomy of a singular leaf of a singular foliation as a sequence of group morphisms from to the of the universal Lie -algebroid of…
Shifted Poisson structures on differentiable stacks
Francesco Bonechi, Nicola Ciccoli, Camille Laurent-Gengoux +1
The purpose of this paper is to investigate shifted Poisson structures in context of differential geometry. The relevant notion is shifted Poisson structures on diffe…
Nijenhuis forms on Lie-infinity algebras associated to Lie algebroids
M. Jawad Azimi, C. Laurent-Gengoux, J. M. Nunes da Costa
Introducing Nijenhuis forms on Lie-infinity algebras gives a general frame to understand deformations of the latter. We give here a Nijenhuis interpretation of a deformation of an…
Cotangent paths as coisotropic subsets for local functions
Camille Laurent-Gengoux, Yahya Turki
We establish a local function version of a classical result claiming that a bivector field on a manifold is Poisson if and only if cotangent paths form a coisotropic set of the…
Lie rackoids
Camille Laurent-Gengoux, Friedrich Wagemann
We define a new differential geometric structure, called Lie rackoid. It relates to Leibniz algebroids exactly as Lie groupoids relate to Lie algebroids. Its main ingredient is a s…
Invariant connections and PBW theorem for Lie groupoid pairs
Camille Laurent-Gengoux, Yannick Voglaire
To a closed wide Lie subgroupoid of a Lie groupoid , i.e. a Lie groupoid pair, we associate an Atiyah class which we interpret as the obstruction to the ex…
Global Action-Angle Variables for Non-Commutative Integrable Systems
Rui L. Fernandes, Camille Laurent-Gengoux, Pol Vanhaecke
In this paper we analyze the obstructions to the existence of global action-angle variables for regular non-commutative integrable systems (NCI systems) on Poisson manifolds. In co…
A cohomological framework for homotopy moment maps
Yael Fregier, Camille Laurent-Gengoux, Marco Zambon
Given a Lie group acting on a manifold preserving a closed -form , the notion of homotopy moment map for this action was introduced in Callies-Fregier-Rogers-Zambon [6]…
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…
Hom-Lie algebroids
Camille Laurent-Gengoux, Joana Teles
We define hom-Lie algebroids, a definition that may seem cumbersome at first, but which is justified, first, by a one-to-one corespondence with hom-Gerstenhaber algebras, a notion…
Hierarchies and compatibility on Courant algebroids
Paulo Antunes, Camille Laurent-Gengoux, Joana M. Nunes da Costa
We extend to the context of Courant algebroids several hierarchies that can be constructed on Poisson-Nijenhuis manifolds. More precisely, we introduce several notions (Poisson-Nij…
Jacobi structures in supergeometric formalism
Paulo dos Santos Antunes, Camille Laurent-Gengoux
We use the supergeometric formalism, more precisely, the so-called "big bracket" (for which brackets and anchors are encoded by functions on some graded symplectic manifold) to add…
Equivariant resolutions of singularities as differential substacks
Camille Laurent-Gengoux
We show that there is an one-to-one correspondence between resolutions (equivariant w.r.t. a Lie groupoid action) of a singular subset of a manifold, and substacks (of a certain ty…
Integration of Holomorphic Lie Algebroids
Camille Laurent-Gengoux, Mathieu Stienon, Ping Xu
We prove that a holomorphic Lie algebroid is integrable if, and only if, its underlying real Lie algebroid is integrable. Thus the integrability criteria of Crainic-Fernandes do al…
Lectures on Poisson groupoids
Camille Laurent-Gengoux, Mathieu Stienon, Ping Xu
In these lecture notes, we give a quick account of the theory of Poisson groupoids and Lie bialgebroids. In particular, we discuss the universal lifting theorem and its application…
Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
Camille Laurent-Gengoux, Mathieu Stienon, Ping Xu
We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in t…
From Lie groupoids to resolutions of singularities. Applications to symplectic and Poisson resolutions
Camille Laurent-Gengoux
We use the techniques of integration of Poisson manifolds into symplectic Lie groupoids to build symplectic resolutions (= desingularizations) of the closure of a symplectic leaf.…
Non Abelian Differentiable Gerbes
Camille Laurent-Gengoux, Mathieu Stienon, Ping Xu
We study non-abelian differentiable gerbes over stacks using the theory of Lie groupoids. More precisely, we develop the theory of connections on Lie groupoid -extensions, which…