GRAPHS OF CURVES ON INFINITE-TYPE SURFACES WITH MAPPING CLASS GROUP ACTIONS

被引：18

作者：

Durham, Matthew Gentry ^{[1
]}

Fanoni, Federica ^{[2
]}

Vlamis, Nicholas G. ^{[3
]}

机构：

[1] Univ Calif Riverside, 900 Univ Ave, Riverside, CA 92521 USA

[2] Heidelberg Univ, Neuenheimer Feld 205, D-69120 Heidelberg, Germany

[3] CUNY Queens Coll, Dept Math, 65-30 Kissena Blvd, Flushing, NY 11367 USA

来源：

ANNALES DE L INSTITUT FOURIER | 2018年 / 68卷 / 06期

基金：

美国国家科学基金会;

关键词：

mapping class groups; surface homeomorphisms; curve graphs; infinite-type surfaces; UNIFORM HYPERBOLICITY; GEOMETRY; ARC;

D O I：

10.5802/aif.3217

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study when the mapping class group of an infinite-type surface S admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on S. We introduce a topological invariant for infinite-type surfaces that determines in many cases whether there is such an action. This allows us to conclude that, as non-locally compact topological groups, many big mapping class groups have nontrivial coarse geometry in the sense of Rosendal.

引用

页码：2581 / 2612

页数：32

共 35 条

[1]

[Anonymous], 1960, Princeton Mathematical Series

[2]

[Anonymous], 1920, Fund. Math, DOI DOI 10.4064/FM-1-1-17-27

[3]

Aramayona J., 2016, MATH Z

[4] ARC AND CURVE GRAPHS FOR INFINITE-TYPE SURFACES [J].

Aramayona, Javier ;

Fossas, Ariadna ;

Parlier, Hugo .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (11) :4995-5006

[5] Hyperbolicity ray graph and quasi-morphisms on a large modular group [J].

Bavard, Juliette .

GEOMETRY & TOPOLOGY, 2016, 20 (01) :491-535

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

Behrstock, Jason ;

Kleiner, Bruce ;

Minsky, Yair ;

Mosher, Lee .

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

[7] Dimension and rank for mapping class groups [J].

Behrstock, Jason A. ;

Minsky, Yair N. .

ANNALS OF MATHEMATICS, 2008, 167 (03) :1055-1077

[8]

Bestvina M., 2010, PUBL MATH-PARIS, V122, P1

[9]

Bestvina M., 2016, COMMUNICATION

[10] LARGE-SCALE RIGIDITY PROPERTIES OF THE MAPPING CLASS GROUPS [J].

Bowditch, Brian H. .

PACIFIC JOURNAL OF MATHEMATICS, 2018, 293 (01) :1-73

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