Uniform local finiteness of the curve graph via subsurface projections
Geometric Topology
2015-11-03 v4
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.
Keywords
Cite
@article{arxiv.1312.5040,
title = {Uniform local finiteness of the curve graph via subsurface projections},
author = {Yohsuke Watanabe},
journal= {arXiv preprint arXiv:1312.5040},
year = {2015}
}
Comments
25 pages. Minor revisions following comments from the referees. Bibliography updated. No mathematical change from v3