Combinatorial suspension for disc-homeomorphisms

François Gautero (1) , Jérôme Los (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 CMI - Centre de Mathématiques et Informatique [Marseille]

For a punctured-disc homeomorphism given combinatorially, we give an algorithmic construction of the suspension flow in the corresponding mapping-torus. In particular one computes explicitly the embedding in the mapping-torus of any finite collection of periodic orbits for this flow. All these orbits are realized as closed braids carried by a branched surface which we construct in the algorithm. Our construction gives a combinatorial proof of the fact that the periodic orbits of such a suspension flow are carried by a same branched-surface.

Mots clés: periodic orbits; braids; knots; templates; branched surfaces; train-tracks; pseudo-Anosov; forcing relation

Domaines: Topologie géométrique [math.GT]; Systèmes dynamiques [math.DS]

François Gautero, Jérôme Los. Combinatorial suspension for disc-homeomorphisms. Journal of Knot Theory and Its Ramifications, 1998, 7 (6), pp.747-795. ⟨hal-00914471⟩