Discrete connection Laplacians
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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.References
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Additional Information
- Svetoslav Zahariev
- Affiliation: Department of Mathematics and Computer Science, Lehman College of CUNY, 250 Bedford Park Boulevard West, Bronx, New York 10468
- Email: szahariev@gc.cuny.edu
- Received by editor(s): July 17, 2007
- Received by editor(s) in revised form: September 13, 2007
- Published electronically: May 19, 2008
- Communicated by: Mikhail Shubin
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3717-3726
- MSC (2000): Primary 58J50
- DOI: https://doi.org/10.1090/S0002-9939-08-09359-3
- MathSciNet review: 2415060