Holonomy on Poisson Manifolds and the Modular Class

Details Holonomy on Poisson Manifolds and the Modular Class Holonomy on Poisson Manifolds and the Modular Class

1998-12-28

arxiv.org/abs/math/9812153v1

Mathematics

Differential Geometry

ams-latex, 19 pages

Scientific paper

We introduce linear holonomy on Poisson manifolds. The linear holonomy of a Poisson structure generalizes the linearized holonomy on a regular symplectic foliation. However, for singular Poisson structures the linear holonomy is defined for the lifts of tangential path to the cotangent bundle (cotangent paths). The linear holonomy is closely related to the modular class studied by A. Weinstein. Namely, the logarithm of the determinant of the linear holonomy is equal to the integral of the modular vector field along such a lift. This assertion relies on the notion of the integral of a vector field along a cotangent path on a Poisson manifold, which is also introduced in the paper. In the second part of the paper we prove that for locally unimodular Poisson manifolds the modular class is an invariant of Morita equivalence.

Affiliated with

Also associated with

No associations

Rating

Holonomy on Poisson Manifolds and the Modular Class does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Holonomy on Poisson Manifolds and the Modular Class, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holonomy on Poisson Manifolds and the Modular Class will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-407385