On the Maximum Poincaré Polynomial, Minimal Morse Functions and Whitehead´s Torsion

This paper is about a generalization of both, the genus of surfaces and the Heegard genus of closed orientable three manifolds, the Maximal Poincar\'e polynomial due to V. Benci and K. A. De Rezende \cite{bdr}. It is also about the related subject minimal Morse functions and the connections of minimal Morse functions to Whitehead's torsion. We establish further properties of the Maximal Poincar\'epolynomial in addition to the ones developed in \cite{bdr}.