Products of Farey graphs are totally geodesic in the pants graph

被引：2

作者：

Taylor, Samuel J. ^{[1
]}

Zupan, Alexander ^{[2
]}

机构：

[1] Yale Univ, Dept Math, 20 Hillhouse Ave, New Haven, CT 06520 USA

[2] Univ Texas Austin, Dept Math, 1 Univ Stn C1200, Austin, TX 78712 USA

来源：

JOURNAL OF TOPOLOGY AND ANALYSIS | 2016年 / 8卷 / 02期

基金：

美国国家科学基金会;

关键词：

Pants graph; totally geodesic; mapping class group; TEICHMULLER SPACE; COMPLEX; VOLUMES; RANK;

D O I：

10.1142/S1793525316500096

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that for a surface Sigma, the subgraph of the pants graph determined by fixing a collection of curves that cut Sigma into pairs of pants, once-punctured tori, and four-times-punctured spheres is totally geodesic. The main theorem resolves a special case of a conjecture made in [2] and has the implication that an embedded product of Farey graphs in any pants graph is totally geodesic. In addition, we show that a pants graph contains a convex n-flat if and only if it contains an n-quasi-flat.

引用

页码：287 / 311

页数：25

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