Existence d’un feuilletage positivement transverse à un homéomorphisme de surface

Abstract

Let F be a homeomorphism of an oriented surface M that is isotopic to the identity. Le Calvez proved that if F admits a lift F ˜ without fixed points to the universal covering of M, then there exists a topological foliation of M transverse to the dynamics. We generalize this result to the case where F ˜ has fixed points. We obtain a singular topological foliation whose singularities are fixed points of F.