论文标题
编织是托里上的缠结
Knotty knits are tangles on tori
论文作者
论文摘要
在本文中，我们概述了一个拓扑框架，用于构建2个周期针织针和一个将针迹结合在一起以形成更复杂的纺织品的代数。我们的拓扑框架可以由某些拓扑“移动”构建，这些拓扑“移动”与编织者创建针迹时所做的“操作”相对应。在编织中，与Jacquard编织不同，一组$ n $循环可以以拓扑的方式合并，以创建与不相关的$ n $针迹。我们将A \ emph {shatch}定义为允许这些可济打结的结构。
In this paper we outline a topological framework for constructing 2-periodic knitted stitches and an algebra for joining stitches together to form more complicated textiles. Our topological framework can be constructed from certain topological "moves" which correspond to "operations" that knitters make when they create a stitch. In knitting, unlike Jacquard weaves, a set of $n$ loops may be combined in topologically nontrivial ways to create $n$ stitches that are not pairwise associated. We define a \emph{swatch} as a construction that allows for these knitable knots.
