22 citations · 53 across the 10 of their papers we have counts for
13 papers · 1 filter
Homotopy of representations up to homotopy
Olivier Brahic, Pedro Frejlich
We propose a general definition of morphism of representations up to homotopy of Lie algebroids, which is be mandated by the requirement that taking cohomology with coefficients in…
Concurring reduction schemes for Dirac structures
Dan Aguero, Alessandro Arsie, Pedro Frejlich +1
The notion of \emph{concurrence} was recently proposed as the natural compatibility relation between Dirac structures, generalizing the commutativity of two Poisson structures. We…
Dirac products and concurring Dirac structures
Pedro Frejlich, David Martínez Torres
We discuss in this note two dual canonical operations on Dirac structures and -- the \emph{tangent product} and the \emph{cotangent product} .…
Normal forms for principal Poisson Hamiltonian spaces
Pedro Frejlich, Ioan Marcut
We prove a normal form theorem for principal Hamiltonian actions on Poisson manifolds around the zero locus of the moment map. The local model is the generalization to Poisson geom…
Coregular submanifolds and Poisson submersions
Lilian C. Brambila, Pedro Frejlich, David Martínez Torres
We analyze \emph{submersions with Poisson fibres}. These are submersions whose total space carries a Poisson structure, on which the ambient Poisson structure pulls back, as a Dira…
Submersions by Lie algebroids
Pedro Frejlich
In this note, we examine the bundle picture of the pullback construction of Lie algebroids. The notion of submersions by Lie algebroids is introduced, which leads to a new proof of…
Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids
Pedro Frejlich
In this note, we prove that intrinsic characteristic classes of Lie algebroids - which in degree one recover the modular class - behave functorially with respect to arbitrary trans…
The homology class of a Poisson transversal
Pedro Frejlich, Ioan Marcut
This note is devoted to the study of the homology class of a compact Poisson transversal in a Poisson manifold. For specific classes of Poisson structures, such as unimodular Poiss…
On dual pairs in Dirac Geometry
Pedro Frejlich, Ioan Marcut
In this note we discuss dual pairs in Dirac geometry. We show that this notion appears naturally when studying the problem of pushing forward a Dirac structure along a surjective s…
Normal forms for Poisson maps and symplectic groupoids around Poisson transversals
Pedro Frejlich, Ioan Marcut
Poisson transversals are those submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In a previous note we proved a normal form…
A note on symplectic topology of -manifolds
Pedro Frejlich, David Martínez Torres, Eva Miranda
A Poisson manifold $(M^{2n},\p)$ is -symplectic if $\bigwedge^n\p$ is transverse to the zero section. In this paper we apply techniques native to Symplectic Topology to address…
The Normal Form Theorem around Poisson Transversals
Pedro Frejlich, Ioan Marcut
We prove a normal form theorem for Poisson structures around Poisson transversals (also called cosymplectic submanifolds), which simultaneously generalizes Weinstein's symplectic n…
A h-principle for symplectic foliations
Rui Loja Fernandes, Pedro Frejlich
We show that a classical result of Gromov in symplectic geometry extends to the context of symplectic foliations, which we regard as a -principle for (regular) Poisson geometry.…