论文标题
极端霍瓦诺夫同源性和结的围长
Extremal Khovanov homology and the girth of a knot
论文作者
论文摘要
我们利用Khovanov和色差同源性之间的关系来确定琼斯多项式的极端Khovanov组和相应的系数。可以使用色相同源性和色度条件来计算链接的积分khovanov同源性的程度取决于其全阳性图的最大周长。在本文中，我们还定义了一个链接的围墙，讨论与其他结的关系以及围绕围栏的可能值。分析周长会导致对任何给定链接的可能的全部状态图的描述；例如，如果一个链接的图表，则相应的all-A图的周长等于$ \ ell> 2 $，而链接的周长等于$ \ ell。
We utilize relations between Khovanov and chromatic graph homology to determine extreme Khovanov groups and corresponding coefficients of the Jones polynomial. The extent to which chromatic homology and chromatic polynomial can be used to compute integral Khovanov homology of a link depends on the maximal girth of its all-positive graphs. In this paper we also define the girth of a link, discuss relations to other knot invariants, and the possible values for girth. Analyzing girth leads to a description of possible all-A state graphs of any given link; e.g., if a link has a diagram such that the girth of the corresponding all-A graph is equal to $\ell>2$, than the girth of the link is equal to $\ell.$
