关于由两个正的多重扭曲生成的群：Teichmueller曲线和Lehmer数
On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number
摘要：
从一个简单的观察瑟斯顿的建设，我们得出了几个有趣的事实，子群的映射类群产生的两个积极的多曲折。特别是，我们确定了所有配置的曲线，相应的群体不能是自由的，并表明，这些子集确定相同的一组Teichmueller曲线的非钝角网格三角形被分类的凯尼恩，Smillie，和Puchta。我们还确定了一个伪Anosov自同构的扩张是Lehmer数，并表明这是最小的考虑中的群体。此外，我们描述了一个连接到工作的McMullen Coxeter组和相关工作的Hironaka建设一个有趣的一类纤维链接。
英文摘要：
From a simple observation about a construction of Thurston, we derive several interesting facts about subgroups of the mapping class group generated by two positive multi-twists. In particular, we identify all configurations of curves for which the corresponding groups fail to be free, and show that a subset of these determine the same set of Teichmueller curves as the non-obtuse lattice triangles which were classified by Kenyon, Smillie, and Puchta. We also identify a pseudo-Anosov automorphism whose dilatation is Lehmer's number, and show that this is minimal for the groups under consideration. In addition, we describe a connection to work of McMullen on Coxeter groups and related work of Hironaka on a construction of an interesting class of fibered links.
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