Global rigidity of some abelian-by-cyclic group actions on 𝕋2

IF 2 1区数学

Geometry & Topology Pub Date : 2019-09-23 DOI:10.2140/gt.2021.25.3133

Sebastián Hurtado, Jinxin Xue

引用次数: 2

Abstract

For groups of diffeomorphisms of $\T^2$ containing an Anosov diffeomorphism, we give a complete classification for polycyclic Abelian-by-Cyclic group actions on $\T^2$ up to both topological conjugacy and smooth conjugacy under mild assumptions. Along the way, we also prove a Tits alternative type theorem for some groups of diffeomorphisms of $\T^2$.

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𝕋2上一些阿贝尔环群的整体刚性

对于$\T^2$的含有Anosov微分同态的微分同态群，在温和的假设下，给出了$\T^2$上的多环阿贝列乘环群作用在拓扑共轭和光滑共轭下的完全分类。在此过程中，我们还证明了$\T^2$的一些微分同态群的Tits可选型定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geometry & Topology 数学-数学

自引率

5.00%

发文量

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.