Transitivity of codimension one Anosov actions of R^k on closed manifolds

Thierry Barbot, Carlos Maquera

Published 2008-07-15, updated 2008-07-29Version 2

In this paper, we define codimension one Anosov actions of $\RR^k, k\geq 2,$ on a closed connected orientable manifold $M$. We prove that if the ambient manifold has dimension greater than $k+2$, then the action is topologically transitive. This generalizes a result of Verjovsky for codimension one Anosov flows.