Poisson cohomology of singular fibrations in dimension 4

TL;DR

This paper investigates how the monodromy of singular fibrations in 4-manifolds influences the Poisson cohomology groups, providing insights into the structure of singular Poisson manifolds.

Contribution

It introduces a detailed analysis of the impact of monodromy on Poisson cohomology in 4-dimensional singular fibrations, a novel aspect in the study of such structures.

Findings

Monodromy affects Poisson cohomology groups significantly.

Classification of singular fibrations based on their Poisson cohomology.

New methods to compute cohomology in singular Poisson structures.

Abstract

It is known that there exist singular Poisson structures in $4$-manifolds, whose symplectic foliation is given by singular fibrations over surfaces. In this work, we describe the effect of the monodromy of the fibration on the Poisson cohomology groups.