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    Université de Fribourg

    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.

    Université de Fribourg

    Curve graphs on surfaces of infinite type

    Fossas, Ariadna ; Parlier, Hugo

    In: Annales Academiae Scientiarum Fennicae Mathematica, 2015, vol. 40, p. 793–801

    We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the graphs we construct are generally connected, infinite diameter and infinite rank.