论文标题
多项式不变式，可以区分结的方向
Polynomial invariants which can distinguish the orientations of knots
论文作者
论文摘要
本文包含第一个结多项式，可以区分经典结的方向，并且不夸大结组的使用。但是他们以几何方式广泛使用子午线和经度。 让$ m $成为常规同位素的拓扑模量空间，对于任何天然数字$ n> 1 $ n> 1 $，是所有n-Cables $ nk $ nk $ nk $ nk $ nk $ nk $ nk $ k $的空间，这些空间是由给定的字符串链接$ t $ twand twest the Infinity the Solid the solid torus the solid of the Infintial of Solid of the Infintial nimpoint of nim the Infinity nimpoint of nim the Infintial nimpoins of nimnity ot nimpoint of nimnity的。首先，我们通过将高斯图公式用于有限型典型不变式，为$ m_n $构建整数有价值的组合1 cocycles。然后，我们观察到我们的1个循环允许将$ nk $的某些交叉固定为1个cocycles的局部参数。最后，通过遵循同位素的交叉点，我们将本地参数转换为一组无序的全局参数。现在，我们在$ m_n $中的规范环上评估了1个循环。结果是$ k $的多项式价值不变式，其中变量由有限类型的不变式和常规的同位素类型的字符串链接$ t $索引。
This paper contains the first knot polynomials which can distinguish the orientations of classical knots and which make no excplicit use of the knot group. But they make extensive use of the meridian and of the longitude in a geometric way. Let $M$ be the topological moduli space of long knots up to regular isotopy, and for any natural number $n > 1$ let $M_n$ be the moduli space of all n-cables $nK$ of framed long knots $K$ which are twisted by a given string link $T$ to close to a knot in the solid torus, with a marked point on the knot at infinity. First we construct integer valued combinatorial 1-cocycles for $M_n$ by using Gauss diagram formulas for finite typ invariants. We observe then that our 1-cocycles allow to fix certain crossings of $nK$ as local parameters of the 1-cocycles. Finally, we transform the local parameter into an unordered set of global parameters by following the crossings in the isotopy. We evaluate now the 1-cocycles on a canonical loop in $M_n$. The outcome are polynomial valued invariants of $K$, where the variables are indexed by finite type invariants and by regular isotopy types of string links $T$.
