Laminations géodésiques plates

Thomas Morzadec (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

Since their introduction by Thurston, geodesic laminations on hyperbolic surfaces occur in many contexts. In this paper, we propose a generalization of geodesic laminations on locally CAT(0) , complete, geodesic metric spaces, whose boundary at infi- nity of the universal cover is endowed with an invariant total cyclic order. Then we study these new objects on surfaces endowed with half-translation structures and on finite metric graphs. The main result of the paper is a theorem of classification of geodesic laminations on a compact surface endowed with a half-translation structure. We also show that every finite metric fat graph, outside four homeomorphism classes, is the support of a geodesic lamination with uncountably many leaves none of which is eventually periodic.

Mots clés: différentielle quadratique holomorphe; feuilletage singulier; surface hyperbolique; Lamination géodésique; surface munie d'une structure de demi-translation

Domaines: Géométrie métrique [math.MG]; Géométrie différentielle [math.DG]

Thomas Morzadec. Laminations géodésiques plates. 2014. ⟨hal-01063448⟩