Poisson structures whose Poisson diffeomorphism group is not locally path-connected

TL;DR

This paper constructs examples of Poisson structures with Poisson diffeomorphism groups that are not locally path-connected, highlighting unusual topological properties in Poisson geometry.

Contribution

It provides the first known examples of Poisson structures with non-locally path-connected diffeomorphism groups, revealing new topological phenomena.

Findings

Poisson diffeomorphism group is not locally path-connected in these examples

Examples demonstrate unexpected topological complexity in Poisson geometry

Highlights limitations of local connectivity assumptions in Poisson symmetry groups

Abstract

We build examples of Poisson structure whose Poisson diffeomorphism group is not locally path-connected.