Discrete connection Laplacians

Abstract

SVETOSLAV ZAHARIEVAbstract. To every Hermitian vector bundle with connection over a compactRiemannian manifold M one can associate a corresponding connection Lapla-cian acting on the sections of the bundle. We define analogous combinatorial,metric dependent Laplacians associated to triangulations of M and prove thattheir spectra converge, as the mesh of the triangulations approaches zero, tothe spectrum of the connection Laplacian.