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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 .

生成讲解博客的中文版本

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