ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

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).

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CNPq

FAPESP[2009/06328-2]

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

FAPESP[2009/13882-6]

FAPESP[2008/02841-4]

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)