Geodesic surfaces in the complement of knots with small crossing number

被引：0

作者：

Le, Khanh ^{[1
]}

Palmer, Rebekah ^{[2
]}

机构：

[1] Rice Univ, Dept Math, 6100 Main St, Houston, TX 77005 USA

[2] Temple Univ, Dept Math, 1805 N Broad St, Philadelphia, PA 19122 USA

来源：

NEW YORK JOURNAL OF MATHEMATICS | 2023年 / 29卷

关键词：

hyperbolic knots; totally geodesic surfaces; SEIFERT SURFACES; HYPERBOLIC KNOT; ARITHMETICITY; SPACES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we investigate the problem of counting totally ge-odesic surfaces in the complement of hyperbolic knots with at most 9 cross-ings. Adapting previous counting techniques of boundary slope and inter-section, we establish uniqueness of a totally geodesic surface for the knots 74 and 935. Extending an obstruction to the existence of totally geodesic sur-faces due to Calegari, we show that there is no totally geodesic surface in the complement of 47 knots.

引用

页码：363 / 401

页数：39

共 50 条

[31] PRIME KNOTS WHOSE ARC INDEX IS SMALLER THAN THE CROSSING NUMBER
Jin, Gyo Taek
Lee, Hwa Jeong
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2012, 21 (10)
[32] Band Surgeries between Knots and Links with Small Crossing Numbers
Ishihara, Kai
Shimokawa, Koya
PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, 2011, (191): : 245 - 255
[33] TUNNEL NUMBER ONE KNOTS, m-SMALL KNOTS AND THE MORIMOTO CONJECTURE
Yang, Guoqiu
Yin, Xunbo
Lei, Fengchun
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 141 (12) : 4391 - 4399
[34] Bounding the crossing number of a graph in terms of the crossing number of a minor with small maximum degree
Garcia-Moreno, E
Salazar, G
JOURNAL OF GRAPH THEORY, 2001, 36 (03) : 168 - 173
[35] Small genus knots in lens spaces have small bridge number
Baker, Kenneth L.
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2006, 6 : 1519 - 1621
[36] The Crossing Number of Two-Maps on Orientable Surfaces
Yong Xiang WU 1
2.Department of Mathematics
Journal of Mathematical Research with Applications, 2011, 31 (04) : 643 - 648
[37] Additivity of handle number and Morse-Novikov number of a-small knots
Manjarrez-Gutierrez, Fabiola
TOPOLOGY AND ITS APPLICATIONS, 2013, 160 (01) : 117 - 125
[38] A Lower Bound for the Crossing Number of Links in Thickened Surfaces
V. V. Tarkaev
Siberian Mathematical Journal, 2018, 59 : 1125 - 1132
[39] The Crossing Number of Two-Maps on Orientable Surfaces
Yong Xiang WU Han REN Tu XU Department of Mathematics Education Resource CenterNingbo PolytechnicZhejiang PRChinaDepartment of MathematicsEast China Normal UniversityShanghai PRChina
数学研究与评论, 2011, 31 (04) : 643 - 648
[40] Intersection of Curves and Crossing Number of Cm× Cn on Surfaces
F. Shahrokhi
O. Sýkora
L. A. Székely
I. Vrt'o
Discrete & Computational Geometry, 1998, 19 : 237 - 247

← 1 2 3 4 5 →