Stability of symplectic leaves

TL;DR

This paper develops computable criteria for the stability of symplectic leaves in Poisson manifolds and extends these results to leaves of Lie algebroids, offering new proofs and a broader perspective.

Contribution

It introduces new, practical criteria for stability in Poisson geometry and Lie algebroids, extending classical stability results with a novel approach.

Findings

Provided computable stability criteria for symplectic leaves

Extended stability analysis to singular leaves of Lie algebroids

Reformulated classical stability results using Poisson geometry

Abstract

We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not only extends but also provides a new approach (and proofs) to the classical stability results for foliations and group actions.