$G$-Invariant Deformations of Almost-Coupling Poisson Structures

TL;DR

This paper investigates a special class of Poisson and Dirac structures on foliated manifolds with compact Lie group actions, focusing on their deformation properties and averaging methods.

Contribution

It introduces the concept of $G$-invariant almost-coupling Poisson structures and explores their deformation theory within the context of group actions.

Findings

Characterization of $G$-invariant almost-coupling Poisson structures

Development of averaging techniques for these structures

Insights into deformation stability under group actions

Abstract

On a foliated manifold equipped with an action of a compact Lie group $G$, we study a class of almost-coupling Poisson and Dirac structures, in the context of deformation theory and the method of averaging.