Discretization of vector bundles and rough Laplacian
Differential Geometry
2007-05-23 v1 Spectral Theory
Abstract
We establish a uniform comparison between the spectrum of the rough Laplacian (acting on sections of a vector bundle of complex rank one or of harmonic curvature) with the spectrum of a discrete operator (a generalization of a discrete magnetic Laplacian added with a potential) acting on a finite dimensional space coming from a discretization process. As an application, we obtain a comparison of the first positive eigenvalue of the rough Laplacian with the holonomy.
Keywords
Cite
@article{arxiv.math/0609595,
title = {Discretization of vector bundles and rough Laplacian},
author = {Tatiana Mantuano},
journal= {arXiv preprint arXiv:math/0609595},
year = {2007}
}