Key points are not available for this paper at this time.
Let F be a co-oriented C² foliation on a closed, oriented 3-manifold. We show that T F can be perturbed to a contact structure with Reeb flow transverse to F if and only if F does not support an invariant transverse measure. The resulting Reeb flow has no contractible orbits. This answers a question of Colin and Honda. The main technical tool in our proof is leafwise Brownian motion which we use to construct good transverse measures for F; this gives a new perspective on the Eliashberg--Thurston theorem.
Jonathan Zung (Fri,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: