Artículos de revistas
ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)
Fecha
2011Registro en:
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.29, n.3, p.803-822, 2011
1078-0947
10.3934/dcds.2011.29.803
Autor
BARBOT, Thierry
MAQUERA, Carlos
Institución
Resumen
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).