Poisson and near-symplectic structures on generalized wrinkled fibrations in dimension 6

TL;DR

This paper demonstrates that generalized broken fibrations and their wrinkled variants in six dimensions admit compatible rank-2 Poisson structures, with indefinite cases also supporting near-symplectic structures, expanding geometric understanding in higher dimensions.

Contribution

It introduces the existence of compatible rank-2 Poisson and near-symplectic structures on generalized and wrinkled fibrations in six dimensions, extending previous lower-dimensional results.

Findings

Generalized broken fibrations admit compatible rank-2 Poisson structures.

Wrinkled fibrations in dimension 6 also admit compatible rank-2 Poisson structures.

Indefinite singularities in these fibrations support near-symplectic structures.

Abstract

We show that generalized broken fibrations in arbitrary dimensions admit rank-2 Poisson structures compatible with the fibration structure. After extending the notion of wrinkled fibration to dimension 6 we prove that these wrinkled fibrations also admit compatible rank-2 Poisson structures. In the cases with indefinite singularities we can provide these wrinkled fibrations in dimension 6 with near-symplectic structures.