Faculté des sciences

Arc and curve graphs for infinite-type surfaces

Aramayona, Javier ; Fossas, Ariadna ; Parlier, Hugo

In: Proceedings of the American Mathematical Society, 2017, vol. 145, no. 11, p. 4995–5006

We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite diameter; this extends a recent result of J. Bavard to a large class of punctured surfaces. Plus

Ajouter à la liste personnelle
    Summary
    We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite diameter; this extends a recent result of J. Bavard to a large class of punctured surfaces.