  In this paper, we consider codimension one Anosov actions of IR^k, k ? 1, on
closed connected orientable manifolds of dimension n+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 IR^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 ? 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.
