CODIMENSION ONE FOLIATIONS WITH COUPLING OF SADDLE SINGULARITIES

On closed manifolds, we investigate smooth foliations with Morse singularities in codimension one. In a dead branch, it has been investigated how to join two saddle singular points with complementary indices. We drive a description of the manifolds exhibiting C center and S saddle singular points in sing(F) satisfying C >= S + 1, alternatively, in the case where C > S - 2k, there are at least k pairs of saddle singular points that are in stable connection. These findings are extension of Camacho-Scardua results, which describe the topology of three and n-dimensional manifolds, which are in fact, an extension of earlier findings by Reeb for foliations with only centre singularities, result of Wagneur for foliations containing Morse singularities and Eells and Kuiper for manifolds containing three singularities for the Morse functions.