## On foliated characteristic classes of transversely symplectic foliations

J. Math. Sci. Univ. Tokyo
Vol. 19 (2012), No. 3, Page 263--280.

Bowden, Jonathan
On foliated characteristic classes of transversely symplectic foliations

Abstract:
Kotschick and Morita recently discovered factorisations of characteristic classes of transversely 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 $\mathbb{R}^{2n}$-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.

Keywords: Partial differential equations, Sobolev spaces, stratified fluid, inner waves, essential spectrum

Mathematics Subject Classification (2010): Primary 57R32, 57R17, 57R20; Secondary 57R50