论文标题
互补的地面表面与小交叉数的互补
Geodesic surfaces in the complement of knots with small crossing number
论文作者
论文摘要
在本文中，我们调查了在双曲结中的补充中完全用9个十字路口计数的完全测量表面的问题。调整边界斜率和交集的先前计数技术，我们建立了打结的完全测量表面的唯一性，$ 7_4 $和$ 9_ {35} $。由于卡莱加里（Calegari），我们表明在47节的补充中没有完全测量的表面，因此扩大了完全大地测量表面的障碍。
In this article, we investigate the problem of counting totally geodesic surfaces in the complement of hyperbolic knots with at most 9 crossings. Adapting previous counting techniques of boundary slope and intersection, we establish uniqueness of a totally geodesic surface for the knots $7_4$ and $9_{35}$. Extending an obstruction to the existence of totally geodesic surfaces due to Calegari, we show that there is no totally geodesic surface in the complement of 47 knots.
