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
收藏
页码：363 / 401
页数：39
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