Poisson fiber bundles and coupling Dirac structures

Contact fiber bundles

We define contact fiber bundles and investigate conditions for the existence of contact structures on the total space of such a bundle. The results are analogous to minimal coupling in symplectic geometry. The two applications are construction of K-contact manifolds generalizing Yamazaki's fiber join construction and a cross-section theorem for contact moment maps

Moser stability for volume forms on noncompact fiber bundles

We prove a stability result for volume forms on fiber bundles with compact base and noncompact fibers. This generalizes the classical results of Moser and Greene--Shiohama, and recent work by the authors.

Compatible Poisson Structures on Fibered $5$-Manifolds

We study a class of Poisson tensors on a fibered manifold which are compatible with the fiber bundle structure by the so-called almost coupling condition. In the case of a $5$-dimensional orientable fibered manifolds with $2$-dimensional bases, we describe a global behavior of almost coupling Poisson tensors and their singularities by using a bigraded factorization of the Jacobi identity. In particular, we present some unimodularity criteria and describe a class of gauge type transformations preserving the almost coupling property.

Reduction of a symplectic-like Lie algebroid with momentum map and its application to fiberwise linear Poisson structures

This article addresses the problem of developing an extension of the Marsden- Weinstein reduction process to symplectic Lie algebroids, and in particular to the case of the symplectic cover of a fiberwise linear Poisson structure, whose reduction process is the analogue to cotangent bundle reduction in the context of Lie algebroids.

椭圆切丛与椭圆Poisson结构的整合

Integration of the elliptic tangent bundle and elliptic Poisson structures

本文显式构造了整合椭圆切丛的Lie群胚，给出了Hausdorff整合的充要拓扑条件，并为椭圆Poisson结构的辛整合提供了显式局部模型。

Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions

On a cotangent bundle $T\sp*G$ of a Lie group $G$ one can describe the standard Liouville form $θ$ and the symplectic form $d θ$ in terms of the right Maurer Cartan form and the left moment mapping (of the right action of $G$ on itself), and also in terms of the left Maurer-Cartan form and the right moment mapping, and also the Poisson structure can be written in related quantities. This leads to a wide class of exact symplectic stuctures on $T\sp*G$ and to Poisson structures by replacing the canonical momenta of the right or left actions of $G$ on itself by arbitrary ones, followed by reducti…