Uniform hyperbolicity of the curve graph via surgery sequences

被引：34

作者：

Clay, Matt ^{[1
]}

Rafi, Kasra

Schleimer, Saul

机构：

[1] Univ Arkansas, Dept Math Sci, Fayetteville, AR 72701 USA

来源：

ALGEBRAIC AND GEOMETRIC TOPOLOGY | 2014年 / 14卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

KLEINIAN SURFACE GROUPS; COMPLEX; CLASSIFICATION; GEOMETRY;

D O I：

10.2140/agt.2014.14.3325

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the curve graph C-(1) (S) is Gromov-hyperbolic with a constant of hyperbolicity independent of the surface S. The proof is based on the proof of hyperbolicity of the free splitting complex by Handel and Mosher, as interpreted by Hilion and Horbez.

引用

页码：3325 / 3344

页数：20

共 20 条

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

Aougab, Tarik .

GEOMETRY & TOPOLOGY, 2013, 17 (05) :2855-2875

[2] Geometry and rigidity of mapping class groups [J].

Behrstock, Jason ;

Kleiner, Bruce ;

Minsky, Yair ;

Mosher, Lee .

GEOMETRY & TOPOLOGY, 2012, 16 (02) :781-888

[3] Hyperbolicity of the complex of free factors [J].

Bestvina, Mladen ;

Feighn, Mark .

ADVANCES IN MATHEMATICS, 2014, 256 :104-155

[4] Intersection numbers and the hyperbolicity of the curve conplex [J].

Bowditch, Brian H. .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2006, 598 :105-129

[5] UNIFORM HYPERBOLICITY OF THE CURVE GRAPHS [J].

Bowditch, Brian H. .

PACIFIC JOURNAL OF MATHEMATICS, 2014, 269 (02) :269-280

[6] ASYMPTOTICS OF WEIL-PETERSSON GEODESICS I: ENDING LAMINATIONS, RECURRENCE, AND FLOWS [J].

Brock, Jeffrey ;

Masur, Howard ;

Minsky, Yair .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2010, 19 (05) :1229-1257

[7] The classification of Kleinian surface groups, II: The Ending Lamination Conjecture [J].

Brock, Jeffrey F. ;

Canary, Richard D. ;

Minsky, Yair N. .

ANNALS OF MATHEMATICS, 2012, 176 (01) :1-149

[8]

Hamenstadt U., 2007, IRMA Lect. Math. Theor. Phys., V11, P447

[9] The free splitting complex of a free group, I: hyperbolicity [J].

Handel, Michael ;

Mosher, Lee .

GEOMETRY & TOPOLOGY, 2013, 17 (03) :1581-1670

[10] THE VIRTUAL COHOMOLOGICAL DIMENSION OF THE MAPPING CLASS GROUP OF AN ORIENTABLE SURFACE [J].

HARER, JL .

INVENTIONES MATHEMATICAE, 1986, 84 (01) :157-176

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