Réseaux ferroviaires et courbes simples sur une surface (Train tracks and simple curves on surfaces).

Athanase Papadopoulos (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We establish algorithmic piecewise-linear formulae for the intersection number of simple closed curves with measured foliations, with respect to train track coordinates. This shows in particular that intersction functions are piecewise linear. This implies that Thurston's embedding of measured foliations space into the space of functions on that space is piecewise-linear, and it gives a new point of view on Thurston's peicewise-linear structure of that space.

Mots clés: train track; measured foliation; geometric intersection function.; geometric intersection function

Domaines: Topologie géométrique [math.GT]

Athanase Papadopoulos. Réseaux ferroviaires et courbes simples sur une surface (Train tracks and simple curves on surfaces).. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 1983, 297 Série I, pp. 565-568. ⟨hal-00141722⟩