Virtually small spectral package of a Riemannian manifold

2020/05/10 by Dan Burghelea, Burghelea, Dan, Yoonweon Lee +1
Computer Science · Mathematics · #35P20 #58J20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Spectral Theory (math.SP) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2005.04700

openalex publication_date 2020/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-Poincaré characteristic of the underlying space and extends the \it Poincaré Duality between harmonic forms and between Betti numbers for a closed oriented Riemannian manifold .

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