Uniform local finiteness of the curve graph via subsurface projections

2013/12/18 by Yohsuke Watanabe, Watanabe, Yohsuke · 2 citations
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GT

paper · pdf · doi:10.48550/arxiv.1312.5040

25 pages. Minor revisions following comments from the referees. Bibliography updated. No mathematical change from v3

openalex publication_date 2013/12/18 · arxiv created 2015/11/01 · arxiv updated 2015/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The curve graphs are not locally finite. In this paper, we show that the curve graphs satisfy a property which is equivalent to graphs being uniformly locally finite via Masur--Minsky's subsurface projections. As a direct application of this study, we show that there exist computable bounds for Bowditch's slices on tight geodesics, which depend only on the surface. As an extension of this application, we define a new class of geodesics, weak tight geodesics, and we also obtain a computable finiteness statement on the cardinalities of the slices on weak tight geodesics.

Cited by

• Intersection numbers in the curve graph with a uniform constant
• Intersection numbers in the curve complex via subsurface projections

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