论文标题
无指导的虚拟Khovanov同源性
Unoriented Virtual Khovanov Homology
论文作者
论文摘要
经典链接的琼斯多项式和Khovanov同源性是不变的，取决于该链接的初步选择。在本文中，我们为无定向虚拟链接提供了Khovanov同源性理论。该同源性的分级欧拉（Euler）特征与虚拟链接的类似定义的无定义的琼斯多项式成正比，这是非经典虚拟链接类别中的一个新不变。无定向的琼斯多项式继续满足通常的jones的重要属性：对于经典链接甚至虚拟链接，评估的无定向的琼斯多项式对链接的组件数量的幂却是两个。作为将本文的主要结果扩展到非古典虚拟链接的一部分，描述了一个用于计算积分Khovanov同源性的新框架，可以在计算机上有效地实现，以有效地实现。我们定义了一个基于无关的khovanov同源性的虚拟链接的非导向的Lee同源性理论。
The Jones polynomial and Khovanov homology of a classical link are invariants that depend upon an initial choice of orientation for the link. In this paper, we give a Khovanov homology theory for unoriented virtual links. The graded Euler characteristic of this homology is proportional to a similarly-defined unoriented Jones polynomial for virtual links, which is a new invariant in the category of non-classical virtual links. The unoriented Jones polynomial continues to satisfy an important property of the usual one: for classical or even virtual links, the unoriented Jones polynomial evaluated at one is two to the power of the number of components of the link. As part of extending the main results of this paper to non-classical virtual links, a new framework for computing integral Khovanov homology is described that can be efficiently and effectively implemented on a computer. We define an unoriented Lee homology theory for virtual links based upon the unoriented version of Khovanov homology.
