论文标题
镜头空间的限制打结
Constrained knots in lens spaces
论文作者
论文摘要
在本文中，我们研究了一个特殊的$（1,1）$结的家族，称为“约束结”，其中包括3杆$ s^3 $中的2个桥结和镜头空间中的简单结。受约束的结被五个整数参数化，并以相应$（1,1）$图中的旋转$^c $结构的分布为特征。受约束结的打结浮子同源性$ \ widehat {hfk} $很薄。我们根据$ \ wideHat {hfk} $的计算以及结组的表现获得了约束结的完整分类。我们提供了许多与$ s^3 $链接的手术构建的约束结的示例，这些结与2桥结和1桥辫子有关。我们还展示了许多约束结的例子，这些结的结与简单的理想三角剖分是可定向双曲线1串歧管。
In this paper, we study a special family of $(1,1)$ knots called constrained knots, which includes 2-bridge knots in the 3-sphere $S^3$ and simple knots in lens spaces. Constrained knots are parameterized by five integers and characterized by the distribution of spin$^c$ structures in the corresponding $(1,1)$ diagrams. The knot Floer homology $\widehat{HFK}$ of a constrained knot is thin. We obtain a complete classification of constrained knots based on the calculation of $\widehat{HFK}$ and presentations of knot groups. We provide many examples of constrained knots constructed from surgeries on links in $S^3$, which are related to 2-bridge knots and 1-bridge braids. We also show many examples of constrained knots whose knot complements are orientable hyperbolic 1-cusped manifolds with simple ideal triangulations.
