#### Volume 25, issue 6 (2021)

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Global rigidity of some abelian-by-cyclic group actions on $\mathbb{T}^2$

### Sebastian Hurtado and Jinxin Xue

Geometry & Topology 25 (2021) 3133–3178
##### Abstract

For groups of diffeomorphisms of ${\mathbb{𝕋}}^{2}$ containing an Anosov diffeomorphism, we give a complete classification for polycyclic abelian-by-cyclic group actions on ${\mathbb{𝕋}}^{2}$ 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 ${\mathbb{𝕋}}^{2}$.

##### Keywords
ABC group actions, Tits alternative, rigidity, Anosov
##### Mathematical Subject Classification
Primary: 37B05, 37C85
##### Publication
Revised: 3 October 2020
Accepted: 4 November 2020
Published: 30 November 2021
Proposed: David M Fisher