ALGEBRAIC ANOSOV ACTIONS OF NILPOTENT LIE GROUPS

Thierry Barbot (1) , Carlos Maquera (2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 Instituto de Ciências Matemáticas e de Computação

In this paper we classify algebraic Anosov actions of nilpotent Lie groups on closed manifolds, extending the previous results by P. Tomter. We show that they are all nil-suspensions over either suspensions of Anosov actions of Z^k on nilmanifolds, or (modified) Weyl chamber actions. We check the validity of the generalized Verjovsky conjecture in this algebraic context. We also point out an intimate relation between algebraic Anosov actions and Cartan subalgebras in general real Lie groups.

Mots clés: Algebraic Anosov action; Cartan subalgebra

Domaines: Systèmes dynamiques [math.DS]

Thierry Barbot, Carlos Maquera. ALGEBRAIC ANOSOV ACTIONS OF NILPOTENT LIE GROUPS. Topology Appl., 2013, 160 (1), pp.199--219. ⟨10.1016/j.topol.2012.10.012⟩. ⟨hal-00713622⟩