5 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…