Automatic structures for torus link groups

The growth of torus link groups

Let $G$ be a finitely generated group with a finite generating set $S$. For $g\in G$, let $l_S(g)$ be the length of the shortest word over $S$ representing $g$. The growth series of $G$ with respect to $S$ is the series $A(t) = \sum_{n=0}^\infty a_n t^n$, where $a_n$ is the number of elements of $G$ with $l_S(g)=n$. If $A(t)$ can be expressed as a rational function of $t$, then $G$ is said to have a rational growth function. We calculate explicitly the rational growth functions of $(p,q)$-torus link groups for any $p, q > 1.$ As an application, we show that their growth rates are Perron number…

J-辫群是环面项链群

J-braid groups are torus necklace groups

本文构造了环面项链链环，证明其链环群为广义J-反射群的辫群，将秩二复辫群与环面纽结群的对应推广至所有不可约秩二复反射群，并证明具有非平凡中心的链环群均为Garside群。

实心环中的伪链环与奇异链环

Pseudo links and singular links in the Solid Torus

本文在实心环中建立伪链环与奇异链环的拓扑理论，证明Alexander与Markov定理的类比，引入伪Hecke代数，为构造HOMFLYPT型不变量奠定基础，并推广括号多项式。

广义环面纽结群的字符簇

Character Varieties of Generalized Torus Knot Groups

本文研究广义环面纽结群的字符簇，证明其G-字符簇道路连通，并计算奇数指数下SL(2,C)-字符簇的不可约分支数。