1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs

被引：60
|
作者：
Hensel, Sebastian [1 ]
Przytycki, Piotr [2 ,3 ]
Webb, Richard C. H. [4 ]
机构：
[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA
[2] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 0B9, Canada
[3] Polish Acad Sci, Inst Math, PL-00656 Warsaw, Poland
[4] UCL, Dept Math, London WC1E 6BT, England
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2015年 / 17卷 / 04期
关键词：
Gromov hyperbolic; slim triangle; curve graph; arc graph; unicorn; KLEINIAN SURFACE GROUPS; GEOMETRY; CLASSIFICATION; CONNECTIVITY; DIMENSION; COMPLEX; SPACE;
D O I：
10.4171/JEMS/517
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces.
引用
收藏
页码：755 / 762
页数：8
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