Title: The homology class of a Poisson transversal,
Abstract: This note is devoted to the study of the homology class of a compact Poisson
transversal in a Poisson manifold. For specific classes of Poisson structures,
such as unimodular Poisson structures and Poisson manifolds with closed leaves,
we prove that all their compact Poisson transversals represent non-trivial
homology classes, generalizing the symplectic case. We discuss several examples
in which this property does not hold, as well as a weaker version of this
property, which holds for log-symplectic structures. Finally, we extend our
results to Dirac geometry.