Algebraic Anosov actions of nilpotent Lie groups

Author(s)

Barbot, Thierry ^[1] ; Maquera, Carlos ^[2]

Affiliation

^[1] Univ Avignon & Pays Vaucluse, LANLG, Fac Sci, F-84000 Avignon - France

^[2] Univ Sao Paulo, Inst Ciencias Mat & Comp, BR-13560970 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Topology and its Applications; v. 160, n. 1, p. 199-219, JAN 1 2013.
• Web of Science Citations: 3

Abstract

In this paper we classify algebraic Anosov actions of nilpotent Lie groups on closed manifolds, extending the previous results by P. Tomter (1970, 1975){[}17,18]. 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. (C) 2012 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems
• Grantee: Jorge Manuel Sotomayor Tello
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 09/06328-2 - Codimension one Anosov actions of R^k
• Grantee: Carlos Alberto Maquera Apaza
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 09/13882-6 - Codimension one Anosov actions of R^k
• Grantee: Carlos Alberto Maquera Apaza
• Support Opportunities: Scholarships abroad - Research