Powers of Dehn twists generating right-angled Artin groups
Powers of Dehn twists generating right-angled Artin groups
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Dehn 的幂扭曲生成直角 Artin 群
DOI：
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发表时间：
2019
影响因子：
0.7
通讯作者：
Donggyun Seo
中科院分区：
文献类型：
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作者：
Donggyun Seo
我们给出了Dehn扭转幂指数的一个界，以生成直角Artin群。确切地说，如果$mathcal{F}$是有限型曲面上成对不同的简单闭曲线的有限集合，如果$N$表示$mathcal{F}$中所有曲线对的交点数的最大，那么我们证明${T_gamma^ N,vert， gamma在mathcal{F}}$中对所有$N geq N^2 + N + 3$产生一个直角Artin群。这扩展了Koberda先前的结果，他证明了一个界的存在可能取决于曲面的潜在双曲结构。在证明过程中，我们得到了在某些情况下仅与曲面的拓扑类型有关的普遍界，这部分地回答了由于Koberda问题。
We give a bound for the exponents of powers of Dehn twists to generate a right-angled Artin group. Precisely, if $mathcal{F}$ is a finite collection of pairwise distinct simple closed curves on a finite type surface and if $N$ denotes the maximum of the intersection numbers of all pairs of curves in $mathcal{F}$, then we prove that ${T_gamma^n ,vert, gamma in mathcal{F} }$ generates a right-angled Artin group for all $n geq N^2 + N + 3$. This extends a previous result of Koberda, who proved the existence of a bound possibly depending on the underlying hyperbolic structure of the surface. In the course of the proof, we obtain a universal bound depending only on the topological type of the surface in certain cases, which partially answers a question due to Koberda.