Transitivity of codimension one Anosov actions of Rᵏ on closed manifolds

الأصل · EN

In this paper, we define codimension one Anosov actions of ᵏ, k≥ 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.