Geodesic
Uniform local finiteness of the curve graph via subsurface projections
Yohsuke Watanabe1
1University of Hawaii, Honolulu, USA
Groups, geometry, and dynamics, Tome 10 (2016) no. 4, pp. 1265-1286

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DOI

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.
DOI : 10.4171/ggd/383
Classification : 57-XX
Mots-clés : Curve complex, subsurface projections, tight geodesics, uniform local finiteness property, weak tight geodesics

Yohsuke Watanabe  1

1 University of Hawaii, Honolulu, USA 
Yohsuke Watanabe. Uniform local finiteness of the curve graph via subsurface projections. Groups, geometry, and dynamics, Tome 10 (2016) no. 4, pp. 1265-1286. doi: 10.4171/ggd/383
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     author = {Yohsuke Watanabe},
     title = {Uniform local finiteness of the curve graph via subsurface projections},
     journal = {Groups, geometry, and dynamics},
     pages = {1265--1286},
     year = {2016},
     volume = {10},
     number = {4},
     doi = {10.4171/ggd/383},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/383/}
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