用两个周期元素生成扩展映射类群

Reid Harris
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引用次数: 0

摘要

曲面 $\Sigma$ 的扩展映射类群被定义为 $\Sigma$ 的(不一定是保向的)同构的同位类群。我们能够证明,当 $n\not=4$ 时,$n$-穿孔球面的扩展映射类群由两个有限序元素精确地生成。我们利用这一结果证明了属 2 曲面的扩展映射类群是由两个有限阶元素生成的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Generating Extended Mapping Class Groups with Two Periodic Elements
The extended mapping class group of a surface $\Sigma$ is defined to be the group of isotopy classes of (not necessarily orientation-preserving) homeomorphisms of $\Sigma$. We are able to show that the extended mapping class group of an $n$-punctured sphere is generated by two elements of finite order exactly when $n\not=4$. We use this result to prove that the extended mapping class group of a genus 2 surface is generated by two elements of finite order.
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