论文标题
通过简单的封闭曲线表征盖子
Characterizing covers via simple closed curves
论文作者
论文摘要
给定两个有限的覆盖物$ p：x \至s $和$ q：y \ y \ y \ to s $的连接，定向的，封闭的表面$ s $属的属，至少$ 2 $，我们试图表征curves升至简单曲线的等价$ p $和$ p $和$ q $。使用Teichmüller理论和曲线综合体，我们表明，如果任何封闭的曲线$γ\ subset S $，$γ$ lifts升至$ x $，并且仅在$ y $时，则两个常规覆盖$ p $和$ q $相当于$ x $的简单封闭曲线。当盖子是阿贝利安时，我们还会给出对等效性的表征，即简单的封闭曲线的功率将其升至封闭曲线。
Given two finite covers $p: X \to S$ and $q: Y \to S$ of a connected, oriented, closed surface $S$ of genus at least $2$, we attempt to characterize the equivalence of $p$ and $q$ in terms of which curves lift to simple curves. Using Teichmüller theory and the complex of curves, we show that two regular covers $p$ and $q$ are equivalent if for any closed curve $γ\subset S$, $γ$ lifts to a simple closed curve on $X$ if and only if it does to $Y$. When the covers are abelian, we also give a characterization of equivalence in terms of which powers of simple closed curves lift to closed curves.
