Laminations g\'eod\'esiques plates mesur\'ees

Abstract

In [Mor], we have introduced a notion of flat laminations on surfaces endowed with a flat structure, similar to geodesic laminations on hyperbolic surfaces. Here is a sequel to this article that aims at defining transversal measures on flat laminations similar to transversal measures on hyperbolic laminations, taking into account that two different leaves of a flat lamination may no longer disjoint. Then, we define a topology on the set of measured flat laminations and show that its projective space is compact. Finally, we define the dual tree to a measured flat lamination.