The Genus of Curve, Pants and Flip Graphs

被引：2

作者：

Parlier, Hugo ^{[1
]}

Petri, Bram ^{[2
]}

机构：

[1] Univ Luxembourg, Math Res Unit, L-4365 Esch Sur Alzette, Luxembourg

[2] Univ Bonn, Math Inst, D-53115 Bonn, Germany

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2018年 / 59卷 / 01期

基金：

瑞士国家科学基金会;

关键词：

Curve graph; Pants graph; Flip graph; Graph genus; Surfaces; KLEINIAN SURFACE GROUPS; RANDOM REGULAR GRAPHS; UNIFORM HYPERBOLICITY; TEICHMULLER SPACE; ASYMPTOTIC NUMBER; AUTOMORPHISMS; CLASSIFICATION; COMPLEXES; VOLUMES;

D O I：

10.1007/s00454-017-9922-7

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This article is about the graph genus of certain well studied graphs in surface theory: the curve, pants and flip graphs. We study both the genus of these graphs and the genus of their quotients by the mapping class group. The full graphs, except for in some low complexity cases, all have infinite genus. The curve graph once quotiented by the mapping class group has the genus of a complete graph so its genus is well known by a theorem of Ringel and Youngs. For the other two graphs we are able to identify the precise growth rate of the graph genus in terms of the genus of the underlying surface. The lower bounds are shown using probabilistic methods.

引用

页码：1 / 30

页数：30

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