Groups, Geometry, and Dynamics

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Volume 10, Issue 4, 2016, pp. 1265–1286
DOI: 10.4171/GGD/383

Published online: 2017-01-26

Uniform local finiteness of the curve graph via subsurface projections

Yohsuke Watanabe[1]

(1) University of Hawaii, Honolulu, USA

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: Curve complex, subsurface projections, tight geodesics, uniform local finiteness property, weak tight geodesics

Watanabe Yohsuke: Uniform local finiteness of the curve graph via subsurface projections. Groups Geom. Dyn. 10 (2016), 1265-1286. doi: 10.4171/GGD/383