2008
DOI: 10.1090/s0002-9939-08-09359-3
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Discrete connection Laplacians

Abstract: 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.

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