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

Hurtado, Sebastian¹ ; Xue, Jinxin²

¹ Department of Mathematics, University of Chicago, Chicago, IL, United States
² Yau Mathematical Sciences Center and Department of Mathematics, Tsinghua University, Beijing, China

Geometry & topology, Tome 25 (2021) no. 6, pp. 3133-3178.

Résumé

For groups of diffeomorphisms of ${\mathbb{𝕋}}^2$ containing an Anosov diffeomorphism, we give 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, we also prove a Tits alternative-type theorem for some groups of diffeomorphisms of ${\mathbb{𝕋}}^2$.

Détail

DOI : 10.2140/gt.2021.25.3133

Keywords: ABC group actions, Tits alternative, rigidity, Anosov

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