Distortion and Tits alternative in smooth mapping class groups
Distortion and Tits alternative in smooth mapping class groups
复制标题
平滑映射类组中的扭曲和山雀替代方案
DOI：
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发表时间：
2015
影响因子：
1.3
通讯作者：
E. Militon
中科院分区：
文献类型：
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作者：
Sebastián Hurtado;E. Militon
本文研究了曲面S相对于给定康托集的光滑映射类群，即S的保持取向的光滑微分同态的同位素类群，它们保持康托集。当康托集是标准三元康托集时，我们证明了由S上的恒等同构的微分同胚组成的子群不包含任何畸变元素。此外，我们为这些群体证明了一个弱的Tits替代方案。
In this article, we study the smooth mapping class group of a surface S relative to a given Cantor set, that is the group of isotopy classes of orientation-preserving smooth diffeomorphisms of S which preserve this Cantor set. When the Cantor set is the standard ternary Cantor set, we prove that the subgroup consisting of diffeomorphisms which are isotopic to the identity on S does not contain any distorted elements. Moreover, we prove a weak Tits alternative for these groups.