论文标题
从圆柱体中的打结到平面结的地图
Maps from knots in the cylinder to flat-virtual knots
论文作者
论文摘要
在本文中，我们解决了如何从圆柱体中的结和变厚的圆环上获取图的图表到一个称为虚拟 - 弗拉特结的虚拟结（概括）的问题。主要结构在圆柱体（圆环）上拍摄了一个图，并增加了一些``看不见''的交叉点，从而产生了一个图表，该图可以正式浸入但不能嵌入（绘制）（绘制）（绘制）（曲线）（圆环），并舒适地生活在较高属的较高属的表面中。这使一个人可以````向后''虚拟理论的不变式变成加厚圆柱体（圆环）中的结理论，在这种理论中，奇偶校验括号和其他图像价值不足不够强。
In the present paper, we address the problem how to get a map from knots in the cylinder and on the thickened torus to some (generalisation of) virtual knots called virtual-flat knots. The main construction takes a diagram on a cylinder (torus) and adds some ``invisible'' crossings which gives rise to a diagram which can be formally immersed but not embedded (drawn) on the cylinder (torus) and living comfortably in thickened surfaces of higher genera. This allows one to ``pull back'' invariants of virtual theory to the theory of knots in the thickened cylinder (torus) where the parity bracket and other picture-valued invariants are not strong enough.
