论文标题
右角链路在增厚的表面
Right-angled links in thickened surfaces
论文作者
论文摘要
传统上，研究了交替的链接，并在$ s^3 $中使用$ s^2 $上的交替图。在本文中，我们考虑在$ s_g \ times i $上交替在高级属表面上交替的链接。我们定义了这样的链接的含义，即正确地被广义完全可实现（RGCR），并表明该属性等同于具有两个完全测量的棋盘表面的链接，相当于每种棋盘表面的链接，该链接等于由一种类型的Polygon组成的链接，并且等于对链接的链接替代投资投影图的一组限制。然后，我们使用这些图表限制来根据其棋盘表面中的多边形对RGCR链接进行分类，并为给定的$ g $属表面的RGCR链路数量提供了界限，并找到一个RGCR结。一路上，我们回答了Champanerkar，Kofman和Purcell提出的问题，内容涉及与圆环上的交替预测联系。
Traditionally, alternating links are studied with alternating diagrams on $S^2$ in $S^3$. In this paper, we consider links which are alternating on higher genus surfaces $S_g$ in $S_g \times I$. We define what it means for such a link to be right-angled generalized completely realizable (RGCR) and show that this property is equivalent to the link having two totally geodesic checkerboard surfaces, equivalent to each checkerboard surface consisting of one type of polygon, and equivalent to a set of restrictions on the link's alternating projection diagram. We then use these diagram restrictions to classify RGCR links according to the polygons in their checkerboard surfaces, provide a bound on the number of RGCR links for a given surface of genus $g$, and find an RGCR knot. Along the way, we answer a question posed by Champanerkar, Kofman, and Purcell about links with alternating projections on the torus.
