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

被引：63

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

页码：755 / 762

页数：8

共 26 条

[1]

Alonso J, 1990, GROUP THEORY GEOMETR, V1991, P3

[2] Uniform hyperbolicity of the graphs of curves [J].