Foliations with Morse singularities

Abstract

In this work we study codimension one smooth foliations with Morse singularities without saddle connections on closed manifolds. We extend the results of [2], [3], which are extension of classical result of Reeb in [15], [17] and the result of E Wagneur [44]. In particular we extend the following result of [2] which says, a closed connected and oriented three dimensional manifold admitting Morse foliation having more center singu- larities than saddles is diffeomorphic to three spahere. We extend its n-dimensional case too which is in [3]. We also Extend Haefliger’s type theorem for S 3. In [2], [3] the results has been proved by using the technique of eliminating trivial center- saddle pairs of singularities. In this work we prove the same results in [2], [3] by coupling and eliminating of pair of complementary saddles.