255 citations · 676 across the 36 of their papers we have counts for
19 papers · 1 filter
Lie Groupoids
Henrique Bursztyn, Matias del Hoyo
A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoi…
Courant-Nijenhuis algebroids
Henrique Bursztyn, Thiago Drummond, Clarice Netto
We introduce Courant 1-derivations, which describe a compatibility between Courant algebroids and linear (1,1)-tensor fields and lead to the notion of Courant-Nijenhuis algebroids.…
Dirac structures and Nijenhuis operators
Henrique Bursztyn, Thiago Drummond, Clarice Netto
We introduce a notion of compatibility between (almost) Dirac structures and (1,1)-tensor fields extending that of Poisson-Nijenhuis structures. We study several properties of the…
Deformation spaces and normal forms around transversals
Francis Bischoff, Henrique Bursztyn, Hudson Lima +1
Given a manifold M with a submanifold N, the deformation space D(M,N) is a manifold with a submersion to R whose zero fiber is the normal bundle, and all other fibers are equal to…
Lie groupoids and the Frolicher-Nijenhuis bracket
Henrique Bursztyn, Thiago Drummond
The space of vector-valued forms on any manifold is a graded Lie algebra with respect to the Frolicher-Nijenhuis bracket. In this paper we consider multiplicative vector-valued for…
Lie theory of multiplicative tensors
Henrique Bursztyn, Thiago Drummond
We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only i…
Lie theory of vector bundles, Poisson geometry and double structures
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
We briefly review our results on the Lie theory underlying vector bundles over Lie groupoids and Lie algebroids, pointing out the role of Poisson geometry in extending these result…
Splitting theorems for Poisson and related structures
Henrique Bursztyn, Hudson Lima, Eckhard Meinrenken
According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson…
Principal actions of stacky Lie groupoids
Henrique Bursztyn, Francesco Noseda, Chenchang Zhu
Stacky Lie groupoids are generalizations of Lie groupoids in which the "space of arrows" of the groupoid is a differentiable stack. In this paper, we consider actions of stacky Lie…
Picard groups of Poisson manifolds
Henrique Bursztyn, Rui Loja Fernandes
For a Poisson manifold we develop systematic methods to compute its Picard group , i.e., its group of self Morita equivalences. We establish a precise relationship betw…
Vector bundles over Lie groupoids and algebroids
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucid…
Generalized Kaehler geometry of instanton moduli spaces
Henrique Bursztyn, Gil R. Cavalcanti, Marco Gualtieri
We prove that Hitchin's generalized Kaehler structure on the moduli space of instantons over a compact, even generalized Kaehler four-manifold may be obtained by generalized Kaehle…
A brief introduction to Dirac manifolds
Henrique Bursztyn
These notes are based on lectures given at the school on Geometric and Topological Methods for Quantum Field Theory, in Villa de Leyva, Colombia, in 2009. We present a basic introd…
Multiplicative forms at the infinitesimal level
Henrique Bursztyn, Alejandro Cabrera
We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear dif…
Linear and multiplicative 2-forms
Henrique Bursztyn, Alejandro Cabrera, Cristian Ortiz
We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of mu…
Morita equivalence of Poisson manifold via stack groupoids
Henrique Bursztyn, Chenchang Zhu
This is a condensed exposition of the results of a future work, based on a talk of the second author at the Oberwolfach workshop "Poisson Geometry", April 30--4 May 2007.
Generalized Kahler and hyper-Kahler quotients
Henrique Bursztyn, Gil R. Cavalcanti, Marco Gualtieri
We develop a theory of reduction for generalized Kahler and hyper-Kahler structures which uses the generalized Riemannian metric in an essential way, and which is not described wit…
Reduction of Courant algebroids and generalized complex structures
Henrique Bursztyn, Gil R. Cavalcanti, Marco Gualtieri
We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized Kähler structures which interpolates between holomorphic r…
Integration of twisted Dirac brackets
H. Bursztyn, M. Crainic, A. Weinstein +1
The correspondence between Poisson structures and symplectic groupoids, analogous to the one of Lie algebras and Lie groups, plays an important role in Poisson geometry; it offers,…