Related papers: Coregular submanifolds and Poisson submersions

A regular Poisson manifold can be described as a foliated space carrying a tangentially symplectic form. Examples of foliations are produced here that are not induced by any Poisson structure although all the basic obstructions vanish.

We study symplectic forms on hypersurface algebroids. These are a broad generalization of the $b^{k}$-Poisson structures studied extensively by Miranda, Scott, and collaborators, and their geometry is intimately related to the group of…

We introduce the concept of partial Poisson structure on a manifold $M$ modelled on a convenient space. This is done by specifying a (weak) subbundle $T^{\prime}M$ of $T^{\ast}M$ and an antisymmetric morphism $P:T^{\prime}M\rightarrow TM$…

We present a generalization of Dirac constraint theory based on the theory of Poisson-Dirac submanifolds. The theory is formulated in a coordinate-free manner while simultaneously relaxing the invertibility condition as seen in standard…

Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson…

We compute the Poisson cohomology of a class of Poisson manifolds that are symplectic away from a collection $D$ of hypersurfaces. These Poisson structures induce a generalization of symplectic and cosymplectic structures, which we call a…

We look at Poisson geometry taking the viewpoint of singular foliations, understood as suitable submodules generated by Hamiltonian vector fields rather than partitions into (symplectic) leaves. The class of Poisson structures which behave…

We describe an averaging procedure on a Dirac manifold, with respect to a class of compatible actions of a compact Lie group. Some averaging theorems on the existence of invariant realizations of Poisson structures around (singular)…

In recent years methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this note it is shown that the latter method is actually…

In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form…

Let (M, {\pi} ) be a Poisson manifold. A Poisson submanifold $P \in M$ gives rise to an algebroid $AP \rightarrow P$, to which we associate certain chomology groups which control formal deformations of {\pi} around P . Assuming that these…

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, in particular, a unifying framework for the study of…

We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be…

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 Poisson structures and Poisson manifolds with closed leaves, we…

This is the first in a series of papers dedicated to the study of Poisson manifolds of compact types (PMCTs). This notion encompasses several classes of Poisson manifolds defined via properties of their symplectic integrations. In this…

This manuscript is essentially a collection of lecture notes which were given by the first author at the Summer School Wisl-2019, Poland and written down by the second author. As the title suggests, the material covered here includes the…

Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems…

We explicitly construct several Poisson structures with compact support. For example, we show that any Poisson structure on $\R^n$ with polynomial coefficients of degree at most two can be modified outside an open ball, such that it becomes…

Classical constrained Hamiltonian theory assumes complete observability of system states, but in reality only partial state information is often available. This paper establishes a complete geometric theoretical framework for handling such…

A smooth manifold hosts different types of submanifolds, including embedded, weakly-embedded, and immersed submanifolds. The notion of an immersed submanifold requires additional structure (namely, the choice of a topology); when this…