Diagram formulas of the Viro-Polyak type for finit degree invariants

On formulas of the Lannes and Viro-Polyak type for the finite degree invariants

Vassiliev's knot invariants can be computed in different ways but many of them as Kontsevich integral are very difficult. We consider more visual diagram formulas of the type Polyak-Viro and give new diagram formula for the two basic Vassiliev invariant of degree 4

$\mathbb{R}^{6k}$中$(4k-1)$维纽结与链环的Goussarov-Polyak-Viro型公式

Goussarov-Polyak-Viro type formulas for $(4k-1)$-dimensional knots and links in $\mathbb{R}^{6k}$

本文借鉴经典纽结有限型不变量的高斯图表示思路，推导了高维球面光滑嵌入的不变量组合公式，给出了Haefliger不变量的对应公式，并证明了相关高维辫子空间的同伦收缩核猜想。

三次情形下的 Goussarov-Polyak-Viro 猜想

Goussarov-Polyak-Viro Conjecture for degree three case

本文显式构造长虚拟纽结三次 Vassiliev 不变量的七个 Gauss 图公式及经典纽结的 23 个公式，证明三次情形下的 Goussarov-Polyak-Viro 猜想。

Explicit formulas for the Vassiliev knot invariants

Vassiliev's knot invariants can be computed in different ways but many of them as Kontsevich integral are very difficult. We consider more visual diagram formulas of the type Polyak-Viro and give new diagram formula for the two basic Vassiliev invariant of degree 4.

从积分到有限型不变量的组合公式——一个案例研究

From integrals to combinatorial formulas of finite type invariants -- a case study

本文将 Casson 纽结不变量的位形空间积分局部化，无需对合技巧即可证明面项消失，并由此推出正则图及花瓣图等多重交叉图的箭头图公式，给出 übercrossing 数新下界。