11 citations · 24 across the 8 of their papers we have counts for
8 papers
Shifted lagrangian structures in Poisson geometry
Daniel Álvarez, Henrique Bursztyn, Miquel Cueca
This paper develops new aspects of the interplay between shifted symplectic geometry and classical Poisson geometry, focusing on lagrangian morphisms into 2-shifted symplectic grou…
Lecture notes on the symplectic geometry of graded manifolds and higher Lie groupoids
Miquel Cueca, Antonio Maglio, Fabricio Valencia
In this work, we study symplectic structures on graded manifolds and their global counterparts, higher Lie groupoids. We begin by introducing the concept of graded manifold, starti…
Homological vector fields over differentiable stacks
Daniel Álvarez, Miquel Cueca
In this work we solve the problem of providing a Morita invariant definition of Lie and Courant algebroids over Lie groupoids. By relying on supergeometry, we view these structures…
A geometric characterization of -manifolds and the Frobenius theorem
Henrique Bursztyn, Miquel Cueca, Rajan Amit Mehta
This paper studies graded manifolds with local coordinates concentrated in non-negative degrees. We provide a canonical description of these objects in terms of classical geometric…
Deformations of Lagrangian -submanifolds
Miquel Cueca, Jonas Schnitzer
In this paper we prove graded versions of the Darboux Theorem and Weinstein's Lagrangian tubular neighbourhood Theorem in order to study the deformation theory of Lagrangian -s…
Dimensional reduction of Courant sigma models and Lie theory of Poisson groupoids
Alejandro Cabrera, Miquel Cueca
We show that the 2d Poisson Sigma Model on a Poisson groupoid arises as an effective theory of the 3d Courant Sigma Model associated to the double of the underlying Lie bialgebroid…
Courant cohomology, Cartan calculus, connections, curvature, characteristic classes
Miquel Cueca, Rajan Amit Mehta
We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential…
The geometry of graded cotangent bundles
Miquel Cueca
Given a vector bundle we study the geometry of the graded manifolds , including their canonical symplectic structures, compatible Q-structures and Lagrangian Q…