ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R-k

Author(s)

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

Affiliation

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

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

• Document type: Journal article
• Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 29, n. 3, p. 803-822, MAR 10 2011.
• Web of Science Citations: 0

Abstract

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n). (AU)

• 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
• 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