Arc and curve graphs for infinite-type surfaces

Javier Aramayona; Ariadna Fossas; Hugo Parlier

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arXiv · 1510.07805

Arc and curve graphs for infinite-type surfaces

Javier Aramayona·Ariadna Fossas·Hugo Parlier

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Abstract

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. Second, we study the subgraph of the curve graph spanned by those elements which intersect a fixed separating curve on the surface. We show that this graph has infinite diameter and geometric rank 3, and thus is not hyperbolic.

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BibTeX RIS

Javier Aramayona, Ariadna Fossas, Hugo Parlier. 2015-11-10. Arc and curve graphs for infinite-type surfaces. https://arxiv.org/abs/1510.07805

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