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

For groups of diffeomorphisms of 𝕋2 containing an Anosov diffeomorphism, we give a complete classification for polycyclic abelian-by-cyclic group actions on 𝕋2 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.

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ABC group actions, Tits alternative, rigidity, Anosov
Mathematical Subject Classification
Primary: 37B05, 37C85
Received: 12 April 2020
Revised: 3 October 2020
Accepted: 4 November 2020
Published: 30 November 2021
Proposed: David M Fisher
Seconded: Mladen Bestvina, Anna Wienhard
Sebastian Hurtado
Department of Mathematics
University of Chicago
Chicago, IL
United States
Jinxin Xue
Yau Mathematical Sciences Center and Department of Mathematics
Tsinghua University