Global rigidity of some abelian-by-cyclic group actions on t2 sebastian hurtado and jinxin xue

For groups of diffeomorphisms of T containing an Anosov diffeomorphism, we give a complete classification for polycyclic Abelian-by-Cyclic group actions on T 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.