论文标题
部分可观测时空混沌系统的无模型预测
Cofinal elements and fractional Dehn twist coefficients
论文作者
论文摘要
我们表明，对于具有正属和一个边界组件的表面$ s $，沿平行于边界的曲线的dehn Twist的映射类是Cofinal，在映射类组$ \ operatatorName {mod}（s）$的每个左顺序中。我们应用了此结果表明，$ \ mathbb {r} $上的特定动作的特定动作的翻译数字是分数dehn twist系数的通常定义 - 当$ \ mathbb {r} $上）是独立于基本操作的$ s $时，$ s $ s $属于大于一个。作为代数的代数，我们提供了一个公式，该公式从$ \ operatotorname {mod}（s）$的任意左订购中恢复同构$ s $的分数Dehn Twist系数。
We show that for a surface $S$ with positive genus and one boundary component, the mapping class of a Dehn twist along a curve parallel to the boundary is cofinal in every left ordering of the mapping class group $\operatorname{Mod}(S)$. We apply this result to show that one of the usual definitions of the fractional Dehn twist coefficient -- via translation numbers of a particular action of $\operatorname{Mod}(S)$ on $\mathbb{R}$ -- is in fact independent of the underlying action when $S$ has genus larger than one. As an algebraic counterpart to this, we provide a formula that recovers the fractional Dehn twist coefficient of a homeomorphism of $S$ from an arbitrary left ordering of $\operatorname{Mod}(S)$.
