Deformation of Morse functions. I (Q1826176)

The onset of this paper is to establish necessary and sufficient conditions for the existence of three types of deformations (homotopic, isotopic and adjoint) between two exact Morse functions i.e. functions whose number of critical points is minimal, on closed simply-connected manifolds. The techniques here used are some natural stratifications, the h-cobordism theorem and the Paley index theorem. This paper extends some related results of the author.