Some remarks on the topology of hyperbolic actions of Rn on n-manifolds

This paper contains some results on the topology of a nondegenerate action of R on a compact connected n-manifold M when the action is totally hyperbolic (i.e. its toric degree is zero). We study the]R-action generated by a fixed vector of R-n, that provides some results on the number of hyperbolic domains and the number of fixed points of the action. We study with more details the case of the 2-sphere, in particular we investigate some combinatorial properties of the associated 4-valent graph embedded in S-2. We also construct hyperbolic actions in dimension 3, on the sphere S-3 and on the projective space RP3. (C) 2017 Elsevier B.V. All rights reserved.