多重曲线图的厚度和相对双曲度

Pub Date : 2022-10-31 DOI:10.1112/topo.12270

Jacob Russell, Kate M. Vokes

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引用次数: 0

摘要

我们证明了任何满足某些自然性质的多曲线图要么是双曲的，要么是相对双曲的，要么是粗的。此外，这种几何特征是由与图的每个顶点相交的一组子曲面决定的。这将先前建立的裤子图和分离曲线图的结果扩展到与曲面相关的广泛图族。

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Thickness and relative hyperbolicity for graphs of multicurves

We prove that any graph of multicurves satisfying certain natural properties is either hyperbolic, relatively hyperbolic, or thick. Further, this geometric characterization is determined by the set of subsurfaces that intersect every vertex of the graph. This extends previously established results for the pants graph and the separating curve graph to a broad family of graphs associated to surfaces.

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