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Global Rigidity of Some Abelian-by-Cyclic group actions on $\T^2$
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classification
math.DSmath.GR
keywords
abelian-by-cyclicactionsconjugacydiffeomorphismsgroupgroupssomealong
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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 $\T^2$.
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