Global rigidity of some abelian-by-cyclic group actions on \(\mathbb{T}^2\) (Q2058833)

The authors consider groups of \(C^r\) diffeomorphisms of the torus \(\mathbb{T}^2\), \(r \geq 2\), containing an Anosov diffeomorphism. The work provides 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, a Tits alternative-type theorem for some groups of diffeomorphisms of \(\mathbb{T}^2\) is provided. The work is related to the previous study in [\textit{A. Wilkinson}, et al., Commun. Math. Phys. 376, No. 2, 1223--1259 (2020; Zbl 1448.37037)].