论文标题
关于legendrian的Khovanov同源性和横向简单结的猜想
Conjectures on the Khovanov Homology of Legendrian and Transversely Simple Knots
论文作者
论文摘要
Kronheimer和Mrowka的定理指出，Khovanov同源性能够检测到UNNENGOT。也就是说，如果一个结具有未结的Khovanov同源性，则相当于它。 Trefoils和人物八结的相似结果。这些是传统简单结中最简单的结。我们猜想Khovanov同源性能够区分传奇和横向简单的结。使用圆环和扭结结，为所有素数提供了数值证据，最多可达19个十字路口。还包括了来自Legendrian结图地图集的猜想的简单结，也没有发现与Khovanov多项式相同的结。
A theorem of Kronheimer and Mrowka states that Khovanov homology is able to detect the unknot. That is, if a knot has the Khovanov homology of the unknot, then it is equivalent to it. Similar results hold for the trefoils and the figure-eight knot. These are the simplest of the Legendrian simple knots. We conjecture that Khovanov homology is able to distinguish Legendrian and Transversely simple knots. Using the torus and twist knots, numerical evidence is provided for all prime knots up to 19 crossings. The conjectured Legendrian simple knots from the Legendrian knot atlas have also been included, and no knots with identical Khovanov polynomials were found.
