The Alexander Method for Infinite-Type Surfaces
The Alexander Method for Infinite-Type Surfaces
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无限型曲面的 Alexander 方法
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Ferrán Valdez
中科院分区：
文献类型：
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作者：
J. Hernández;Israel Morales;Ferrán Valdez
证明了对任意无限型可定向曲面S，S中存在本质曲线{Gamma}的集合，使得保持{Gamma}元素的合痕类的同胚与恒等式是同构的.集合{Gamma}在S的曲线复形C（S）中可数且有无穷补。由此得到S的扩张映射类群在C（S）上的自然作用是忠实的。
We prove that for any infinite-type orientable surface S there exists a collection of essential curves {Gamma} in S such that any homeomorphism that preserves the isotopy classes of the elements of {Gamma} is isotopic to the identity. The collection {Gamma} is countable and has infinite complement in C(S), the curve complex of S. As a consequence we obtain that the natural action of the extended mapping class group of S on C(S) is faithful.