论文标题
球形曲线和Östlund猜想的新变形
New deformations on spherical curves and Östlund Conjecture
论文作者
论文摘要
2018年，Funakoshi，Hashizume，Ito，Kobayashi和Murai使用了称为变形型$α$的球形曲线变形。然后，表明，如果两个球形曲线$ p $和$ p'$在由RI型和RIII类型的变形的关系下等效，直到具有环境同位素，并且满足某些条件，那么$ p'$由$ p $从$ p $中获得的有限序列$ p $从$ p $中获得。在本文中，我们引入了一种新型的球形曲线变形，称为$β$的变形。本文的主要结果是：两条球形曲线$ p $和$ p'$等于（可能是空的）RI型变形（可能是空的）变形，并且仅在减少（P）和减少（P）和减少（P'）时，RIII类型的单个变形均与环境同位素相同，而（p）和降低（p'）由$ riii，type $ a $ a;减少（Q）是球形曲线，它不包含从球形曲线$ Q $获得的$ 1 $ -GON，这是通过将RI类型的变形施加到环境同位素的。
In 2018, Funakoshi, Hashizume, Ito, Kobayashi, and Murai used a deformation of spherical curves called deformation type $α$. Then, it was showed that if two spherical curves $P$ and $P'$ are equivalent under the relation consisting of deformations of type RI and type RIII up to ambient isotopy, and satisfy certain conditions, then $P'$ is obtained from $P$ by a finite sequence of deformations of type $α$. In this paper, we introduce a new type of deformations of spherical curves, called deformation of type $β$. The main result of this paper is: Two spherical curves $P$ and $P'$ are equivalent under (possibly empty) deformations of type RI and a single deformation of type RIII up to ambient isotopy if and only if reduced(P) and reduced(P') are transformed each other by exactly one deformation which is of type RIII, type $α$, or type $β$ up to ambient isotopy, where reduced(Q) is the spherical curve which does not contain a $1$-gon obtained from a spherical curve $Q$ by applying deformations of type RI up to ambient isotopy.
