虚拟弦的覆盖物、复合物和线缆
Coverings, composites and cables of virtual strings
摘要：
虚串可以定义为平面图在某种图移下的一个等价类。虚拟字符串与虚拟结相关，因为对虚拟结图的简单操作产生虚拟字符串的图。在本文中，我们考虑三个操作的虚拟字符串或虚拟字符串产生另一个虚拟字符串，即覆盖，组成和电缆。特别是，我们研究虚拟字符串不变的覆盖操作。我们还展示了一个复合虚拟字符串的基础矩阵是如何与其组件的基础矩阵，纠正Turaev的结果。最后，我们调查电缆下发生了什么，一些不变量定义的Turaev。
英文摘要：
A virtual string can be defined as an equivalence class of planar diagrams under certain kinds of diagrammatic moves. Virtual strings are related to virtual knots in that a simple operation on a virtual knot diagram produces a diagram for a virtual string. In this paper we consider three operations on a virtual string or virtual strings which produce another virtual string, namely covering, composition and cabling. In particular we study virtual strings unchanged by the covering operation. We also show how the based matrix of a composite virtual string is related to the based matrices of its components, correcting a result by Turaev. Finally we investigate what happens under cabling to some invariants defined by Turaev.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
