Discretization of vector bundles and rough Laplacian

Details Discretization of vector bundles and rough Laplacian Discretization of vector bundles and rough Laplacian

2006-09-21

arxiv.org/abs/math/0609595v1

Mathematics

Differential Geometry

Scientific paper

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.

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