Bar codes of persistent cohomology and Arrhenius law for p-forms

Abstract

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.

References in corpus (5)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Persistent homology and Floer-Novikov theory
• Low temperature asymptotics for Quasi-Stationary Distributions in a bounded domain
• Barcodes and area-preserving homeomorphisms
• Small eigenvalues of the Witten Laplacian with Dirichlet boundary conditions: the case with critical points on the boundary