English

Global Rigidity of Some Abelian-by-Cyclic group actions on $\T^2$

Dynamical Systems 2021-12-08 v2 Group Theory

Abstract

For groups of diffeomorphisms of \T2\T^2 containing an Anosov diffeomorphism, we give a complete classification for polycyclic Abelian-by-Cyclic group actions on \T2\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 \T2\T^2.

Keywords

Cite

@article{arxiv.1909.10112,
  title  = {Global Rigidity of Some Abelian-by-Cyclic group actions on $\T^2$},
  author = {Sebastian Hurtado and Jinxin Xue},
  journal= {arXiv preprint arXiv:1909.10112},
  year   = {2021}
}

Comments

To appear in Geometry & Topology, revisions according to the referee report from he old version titled "A Tits alternative for surface group diffeomorphisms and Abelian-by-Cyclic actions on surfaces containing an Anosov diffeomorphism"