Farey polytopes and continued fractions associated with discrete hyperbolic groups

被引：19
作者：
Vulakh, LY [1 ]
机构：
[1] Cooper Union Adv Sci & Art, Dept Math, New York, NY 10003 USA
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1999年 / 351卷 / 06期
关键词：
diophantine approximation; Clifford algebra; hyperbolic geometry;
D O I：
10.1090/S0002-9947-99-02151-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The known definitions of Farey polytopes and continued fractions are generalized and applied to diophantine approximation in n-dimensional euclidean spaces. A generalized Remak-Rogers isolation theorem is proved and applied to show that certain Hurwitz constants for discrete groups acting in a hyperbolic space are isolated. The approximation constant for the imaginary quadratic field of discriminant -15 is found.
引用
收藏
页码：2295 / 2323
页数：29
相关论文
共 37 条
[1]  
Beardon A. F., 1983, GEOMETRY DISCRETE GR
[2]   LIMIT POINTS OF KLEINIAN GROUPS AND FINITE SIDED FUNDAMENTAL POLYHEDRA [J].
BEARDON, AF ;
MASKIT, B .
ACTA MATHEMATICA, 1974, 132 (1-2) :1-12
[3]  
BENSON CT, 1985, FINITE REFLECTION GR
[4]  
Bianchi L., 1892, MATH ANN, V40, P332
[5]  
BOREL E, 1903, J MATH PURE APPL, V9, P329
[6]   POLYHEDRAL GROUPS AND GRAPH AMALGAMATION PRODUCTS [J].
BRUNNER, AM ;
LEE, YW ;
WIELENBERG, NJ .
TOPOLOGY AND ITS APPLICATIONS, 1985, 20 (03) :289-304
[7]  
Cassels J. W. S., 1957, An Introduction to Diophantine Approximation
[8]  
Conway J., 2010, Sphere Packings, Lattices and Groups, DOI DOI 10.1007/978-1-4757-2016-7
[9]  
Coxeter H. S. M., 1973, REGULAR POLYTOPES
[10]  
CUSICK TW, 1989, MATH SURVEYS MONOS, V30
1234