Discrete Connection Laplacians
Spectral Theory
2016-02-23 v4 Differential Geometry
Abstract
To every Hermitian vector bundle with connection over a compact Riemannian manifold one can associate a corresponding connection Laplacian acting on the sections of the bundle. We define analogous combinatorial metric dependent Laplacians associated to triangulations of and prove that their spectra converge, as the mesh of the triangulations approaches zero, to the spectrum of the connection Laplacian.
Cite
@article{arxiv.math/0609464,
title = {Discrete Connection Laplacians},
author = {Svetoslav Zahariev},
journal= {arXiv preprint arXiv:math/0609464},
year = {2016}
}
Comments
Final version, to appear in Proc. Amer. Math. Soc