Discrete Connection Laplacians

Details Discrete Connection Laplacians Discrete Connection Laplacians

2006-09-16

arxiv.org/abs/math/0609464v4

Mathematics

Spectral Theory

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

Scientific paper

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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