Building hyperbolic metrics suited to closed curves and applications to lifting simply
Building hyperbolic metrics suited to closed curves and applications to lifting simply
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构建适合闭合曲线的双曲指标以及简单提升的应用
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Jenya Sapir
中科院分区：
文献类型：
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作者：
Tarik Aougab;Jonah Gaster;Priyam Patel;Jenya Sapir
设γ是在具有负欧拉特征的曲面S上至多有k个自相交的本质闭曲线。本文构造了一个双曲度量
ho$，其中$gamma$的长度最多为$M cdot sqrt{k}$，其中$M$是仅取决于$mathcal{S}$的拓扑的常数。此外，$的注入半径
ho$至少为$1/（2sqrt{k}）$。这就产生了线性上界，在覆盖的最小度上，$gamma$作为一个简单的闭合曲线提升（即简单提升）。我们还证明了，如果$gamma$是尖点双曲曲面$mathcal{S}$上的一条长度不超过$L$的闭曲线，则存在一个次数不超过$N cdot L cdot e^{L/2}$的$mathcal{S}$覆盖，其中$N$仅依赖于$mathcal{S}$的拓扑。
Let $gamma$ be an essential closed curve with at most $k$ self-intersections on a surface $mathcal{S}$ with negative Euler characteristic. In this paper, we construct a hyperbolic metric $
ho$ for which $gamma$ has length at most $M cdot sqrt{k}$, where $M$ is a constant depending only on the topology of $mathcal{S}$. Moreover, the injectivity radius of $
ho$ is at least $1/(2sqrt{k})$. This yields linear upper bounds in terms of self-intersection number on the minimum degree of a cover to which $gamma$ lifts as a simple closed curve (i.e. lifts simply). We also show that if $gamma$ is a closed curve with length at most $L$ on a cusped hyperbolic surface $mathcal{S}$, then there exists a cover of $mathcal{S}$ of degree at most $N cdot L cdot e^{L/2}$ to which $gamma$ lifts simply, for $N$ depending only on the topology of $mathcal{S}$.
自由群的本原指数函数，以及解开双曲曲面上的闭合曲线。
DOI：
10.1017/s0305004117000755
发表时间：
2019
影响因子：
0.8
作者：
GUPTA, NEHA;KAPOVICH, ILYA
通讯作者：
KAPOVICH, ILYA