255 citations · 676 across the 36 of their papers we have counts for
11 papers · 1 filter
Graded geometry and generalized reduction
Henrique Bursztyn, Alberto S. Cattaneo, Rajan Amit Mehta +1
We present general reduction procedures for Courant, Dirac and generalized complex structures, in particular when a group of symmetries is acting. We do so by taking the graded sym…
Poisson double structures
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We…
Morita equivalence of formal Poisson structures
Henrique Bursztyn, Inocencio Ortiz, Stefan Waldmann
We extend the notion of Morita equivalence of Poisson manifolds to the setting of {\em formal} Poisson structures, i.e., formal power series of bivector fields $π=π_0 + λπ_1 +\cdot…
Dirac geometry and integration of Poisson homogeneous spaces
Henrique Bursztyn, David Iglesias-Ponte, Jiang-Hua Lu
Using tools from Dirac geometry and through an explicit construction, we show that every Poisson homogeneous space of any Poisson Lie group admits an integration to a symplectic gr…
On higher Dirac structures
Henrique Bursztyn, Nicolas Martinez Alba, Roberto Rubio
We study higher-order analogues of Dirac structures, extending the multisymplectic structures that arise in field theory. We define higher Dirac structures as involutive subbundles…
Multisymplectic geometry and Lie groupoids
Henrique Bursztyn, Alejandro Cabrera, David Iglesias
We study higher-degree generalizations of symplectic groupoids, referred to as {\em multisymplectic groupoids}. Recalling that Poisson structures may be viewed as infinitesimal cou…