论文标题
亚历山大和马尔可夫定理虚拟涂鸦
Alexander and Markov theorems for virtual doodles
论文作者
论文摘要
可以认为，在封闭式表面上没有三个或更高相交的有限浸泡圆圈的某些同位素类别可以将其视为虚拟结理论的平面类似物，其中零属的情况与经典结理论相对应。亚历山大（Alexander）和马尔可夫定理（Markov theorems）为零属案例定理，群体的作用是由双胞胎组扮演的角色，这是一类直角的高倾角群体，它们仅具有相当多的交换性关系。本文的目的是证明亚历山大和马尔可夫定理的较高属案例，其中群体的作用是由一个称为虚拟双胞胎组的新组扮演的，这些小组以自然的方式扩展了双胞胎组。
Study of certain isotopy classes of a finite collection of immersed circles without triple or higher intersections on closed oriented surfaces can be thought of as a planar analogue of virtual knot theory where the genus zero case corresponds to classical knot theory. Alexander and Markov theorems for the genus zero case are known where the role of groups is played by twin groups, a class of right angled Coxeter groups with only far commutativity relations. The purpose of this paper is to prove Alexander and Markov theorems for higher genus case where the role of groups is played by a new class of groups called virtual twin groups which extends twin groups in a natural way.
