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

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 $\T^2$.

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"

References in corpus (5)

• $C^1$-actions of Baumslag-Solitar groups on $S^1$
• Entropy zero area preserving diffeomorphisms of $S^2$
• Rigidity of some abelian-by-cyclic solvable group actions on ${\mathbb{T}}^N$
• Rigidity of certain solvable actions on the sphere
• Small $C^1$ actions of semidirect products on compact manifolds