Discrete Connection Laplacians

Abstract

To every Hermitian vector bundle with connection over a compact Riemannian manifold $M$ 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 $M$ and prove that their spectra converge, as the mesh of the triangulations approaches zero, to the spectrum of the connection Laplacian.

Final version, to appear in Proc. Amer. Math. Soc

References in corpus (2)

• Geometric Structures on the Cochains of a Manifold
• Discretization of vector bundles and rough Laplacian