2020/02/17 by Dorian Le Peutrec, Peutrec, Dorian Le, Francis Nier +4 · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Analysis of PDEs (math.AP) #Bar (unit) #Cohomology #Combinatorics #Computer science #Connection (principal bundle) #Differential Geometry (math.DG) #Eigenvalues and eigenvectors #FOS: Mathematics #FOS: Physical sciences #Function (biology) #Geometry #Homotopy and Cohomology in Algebraic Topology #Laplace operator #Limit (mathematics) #Logarithm #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Morse code #Morse theory #Physics #Probability (math.PR) #Pure mathematics #Quantum mechanics #Space (punctuation) #Topological and Geometric Data Analysis #Topology (electrical circuits) #math-ph #math.AP #math.AT #math.DG #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.2002.06949
published in arXiv (Cornell University) (Cornell University)
arxiv created 2020/02/17 · openalex publication_date 2020/02/17 · arxiv updated 2020/02/18 · openalex created_date 2020/02/24 · openalex updated_date 2026/07/30
This article shows that counting or computing the small eigenvalues of the Witten Laplacian in the semi-classical limit can be done without assuming that the potential is a Morse function as the authors did in [LNV]. In connection with persistent cohomology, we prove that the rescaled logarithms of these small eigenvalues are asymptotically determined by the lengths of the bar code of the function f. In particular, this proves that these quantities are stable in the C 0 topology on the space of functions. Additionally, our analysis provides a general method for computing the subexponential corrections in a large number of cases.