On foliated characteristic classes of transversally symplectic foliations

TL;DR

This paper presents an alternative method for constructing characteristic classes of transversally symplectic foliations, demonstrating these classes can be non-trivial even in topologically trivial bundles, indicating they contain more than just topological information.

Contribution

It introduces a new construction of factorisations of characteristic classes and provides examples showing these classes are non-trivial in topologically trivial cases.

Findings

Characteristic classes can be non-trivial in topologically trivial bundles.

New construction of factorisations of characteristic classes.

Foliated cohomology classes carry non-topological information.

Abstract

Kotschick and Morita recently discovered factorisations of characteristic classes of transversally symplectic foliations that yield new characteristic classes in foliated cohomology. We describe an alternative construction of such factorisations and construct examples of topologically trivial foliated vector bundles for which these characteristic classes are non-trivial. This shows that the foliated cohomology classes of Kotschick and Morita carry information that is not merely topological.