On simultaneous conjugacies of pairs of transverse foliations of the torus

Abstract

We prove in this note that two pairs of transverse minimal topological foliations of the torus are individually conjugated if, and only if they are simultaneously conjugated.

I was informed, after posting this preprint on arXiv, that its main result was already proved in the paper "Classification of Supertransitive 2-Webs on Surfaces", by Aranson, S.K., Grines, V.Z. and Kaimanovich, V.A, Journal of Dynamical and Control Systems 9, 455-468 (2003)