Two-generator discrete subgroups of Isom(H2) containing orientation-reversing elements

被引：28

作者：

Klimenko, E

Sakuma, M

机构：

[1] Russian Acad Sci, Inst Math, Siberian Branch, Novosibirsk 630090, Russia

[2] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 560, Japan

来源：

GEOMETRIAE DEDICATA | 1998年 / 72卷 / 03期

关键词：

extended triangle group; triangle group; unknotting tunnel;

D O I：

10.1023/A:1005032526329

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f and g be elements of the isometry group Isom(H-2) of the hyperbolic plane H-2, and assume that one of them is orientation-reversing. We determine when the group [f, g] they generate is discrete; in particular, we obtain the classification of such groups. As an application to knot theory, we completely determine the tunnel number one Montesinos knots.

引用

页码：247 / 282

页数：36

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