CUSP STRUCTURES OF ALTERNATING LINKS

被引：17
作者：
AITCHISON, IR
LUMSDEN, E
RUBINSTEIN, JH
机构：
[1] Department of Mathematics, University of Melbourne, Parkville, 3052, Victoria
来源：
INVENTIONES MATHEMATICAE | 1992年 / 109卷 / 03期
关键词：
D O I：
10.1007/BF01232034
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An alternating link L(r) is canonically associated with every finite, connected, planar graph-GAMMA. The natural ideal polyhedral decomposition of the complement Of L(r) is investigated. Natural singular geometric structures exist on S3-L(r), with respect to which the geometry of the cusp has a shape reflecting the combinatorics of the underlying link projection. For the class of 'balanced graphs', this induces a flat structure on peripheral tori modelled on the tessellation of the plane by equilateral triangles. Examples of links containing immersed, closed pi-1-injective surfaces in their complements are given. These surfaces persist after 'most' surgeries on the link, the resulting closed 3-manifolds consequently being determined by their fundamental groups.
引用
收藏
页码：473 / 494
页数：22
相关论文
共 26 条
[1]  
AITCHISON IR, 1990, GEOMETRY LOW DIMENSI, V2, P127
[2]  
AITCHISON IR, UNPUB POLYHEDRAL MET
[3]  
AITCHISON IR, 1990, IN PRESS P INT C KNO
[4]  
AITCHISON IR, IN PRESS TOPOLOGY, V90
[5]  
Ballman W., 1985, MANIFOLDS NONPOSITIV
[6]  
BLEILER S, 1990, IN PRESS P INT C KNO
[7]  
Coxeter H. S. M, 1948, REGULAR POLYTOPES
[8]  
COXETER HSM, 1956, 1954 P ICM
[9]  
DELAHARPE P, 1986, ENSEIGN MATH, V32, P271
[10]   PINCHING CONSTANTS FOR HYPERBOLIC MANIFOLDS [J].
GROMOV, M ;
THURSTON, W .
INVENTIONES MATHEMATICAE, 1987, 89 (01) :1-12
123