Virtually small spectral package of a Riemannian manifold

Abstract

For a Morse function on a closed orientable Riemannian manifold one introduces the {\it virtually small spectral package} an analytic object consisting of a finite number of analytic quantities derived from the pair, {\it Riemannian metric, Morse function\} which, in principle, can be calculated. One shows that they determine the {\it Torsion } of the underlying space, a parallel to the result that the dimensions of the spaces of harmonic forms calculate the {\it Euler-Poincar\'e characteristic} of the underlying space and extends the {\it Poincar\'e Duality} between harmonic forms and between Betti numbers for a closed oriented Riemannian manifold .