Non-discrete complex hyperbolic triangle groups of type (m, m, ∞)

被引：2
作者：
Pratoussevitch, Anna [1 ]
机构：
[1] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England
来源：
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2011年 / 43卷
关键词：
D O I：
10.1112/blms/bdq107
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note we prove that a complex hyperbolic triangle group of type (m, m, infinity), that is, a group of isometries of the complex hyperbolic plane, generated by complex reflections in three complex geodesics meeting at angles pi/m, pi/m and 0, is not discrete if the product of the three generators is regular elliptic.
引用
收藏
页码：359 / 363
页数：5
相关论文
共 50 条
[31]   Mirror stabilizers for lattice complex hyperbolic triangle groups [J].
Deraux, Martin .
GEOMETRIAE DEDICATA, 2024, 218 (03)
[32]   UNFAITHFUL COMPLEX HYPERBOLIC TRIANGLE GROUPS, I: INVOLUTIONS [J].
Parker, John R. .
PACIFIC JOURNAL OF MATHEMATICS, 2008, 238 (01) :145-169
[33]   COMPLEX HYPERBOLIC (3, 3, n) TRIANGLE GROUPS [J].
Parker, John R. ;
Wang, Jieyan ;
Xie, Baohua .
PACIFIC JOURNAL OF MATHEMATICS, 2016, 280 (02) :433-453
[34]   The Limit Set for Discrete Complex Hyperbolic Groups [J].
Cano, Angel ;
Liu, Bingyuan ;
Lopez, Marlon M. .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2017, 66 (03) :927-948
[35]   UNFAITHFUL COMPLEX HYPERBOLIC TRIANGLE GROUPS, III: ARITHMETICITY AND COMMENSURABILITY [J].
Paupert, Julien .
PACIFIC JOURNAL OF MATHEMATICS, 2010, 245 (02) :359-372
[36]   On Subgroups Finite Index in Complex Hyperbolic Lattice Triangle Groups [J].
Deraux, Martin .
EXPERIMENTAL MATHEMATICS, 2024, 33 (03) :456-481
[37]   NON-DISCRETE FIGURATION IN TURNER,J.M.W. PETWORTH SERIES AND IN BROWNING,ROBERT POETRY [J].
COLUMBUS, CK .
STUDIES IN BROWNING AND HIS CIRCLE, 1976, 4 (02) :9-25
[38]   Free subgroups in certain generalized triangle groups of type (2, m, 2) [J].
Howie, J ;
Williams, G .
GEOMETRIAE DEDICATA, 2006, 119 (01) :181-197
[39]   Free Subgroups in Certain Generalized Triangle Groups of Type (2, m, 2) [J].
James Howie ;
Gerald Williams .
Geometriae Dedicata, 2006, 119 :181-197
[40]   UNFAITHFUL COMPLEX HYPERBOLIC TRIANGLE GROUPS, II: HIGHER ORDER REFLECTIONS [J].
Parker, John R. ;
Paupert, Julien .
PACIFIC JOURNAL OF MATHEMATICS, 2009, 239 (02) :357-389
12345