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

Hurtado, Sebastian; Xue, Jinxin

doi:10.2140/gt.2021.25.3133

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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

DOI: 10.2140/gt.2021.25.3133

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 $𝕋^{2}$ .

Keywords

ABC group actions, Tits alternative, rigidity, Anosov

Mathematical Subject Classification

Primary: 37B05, 37C85

References

Publication

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

Authors

Sebastian Hurtado
Department of Mathematics University of Chicago Chicago, IL United States

Jinxin Xue
Yau Mathematical Sciences Center and Department of Mathematics Tsinghua University Beijing China

Volume 25, issue 6 (2021)