Every Infinite order mapping class has an infinite order action on the homology of some finite cover
Every Infinite order mapping class has an infinite order action on the homology of some finite cover
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每个无限阶映射类对某些有限覆盖的同源性具有无限阶作用
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Asaf Hadari
中科院分区：
文献类型：
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作者：
Asaf Hadari
我们证明了以下著名的猜想：设$\Sigma$是一个有限型的定向曲面，其基本群是一个非交换自由群。设$\phi \in \texample {Mod}（\Sigma）$是一个无限阶映射类。则存在一个有限的可解覆盖$\widehat{\Sigma} \to \Sigma$，和一个提升$\widehat{\phi}$使得$\widehat{\phi}$对$H_1（\widehat{\Sigma}，\mathbb{Z}）$的作用具有无穷阶。我们的主要工具是同调阴影理论，这是作者以前开发的，和傅立叶分析
We prove the following well known conjecture: let $\Sigma$ be an oriented surface of finite type whose fundamental group is a nonabelian free group. Let $\phi \in \textup{Mod}(\Sigma)$ be a an infinite order mapping class. Then there exists a finite solvable cover $\widehat{\Sigma} \to \Sigma$, and a lift $\widehat{\phi}$ of $\phi$ such that the action of $\widehat{\phi}$ on $H_1(\widehat{\Sigma}, \mathbb{Z})$ has infinite order. Our main tools are the theory of homological shadows, which was previously developed by the author, and Fourier analysis
DOI：
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发表时间：
2005
期刊：
Kobe Journal of Mathematics 22
影响因子：
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作者：
Ando;R.;N.Kame;T.Yamashita;佐藤 靖;佐藤 靖;Yasushi Sato;Yasushi Sato;Yasushi Sato;Yasushi Sato;Yasushi Sato;佐藤 靖;佐藤 靖;佐藤 靖;佐藤 靖;Masaaki SUZUKI
通讯作者：
Masaaki SUZUKI