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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Discrete connection Laplacians


Author: Svetoslav Zahariev
Journal: Proc. Amer. Math. Soc. 136 (2008), 3717-3726
MSC (2000): Primary 58J50
Published electronically: May 19, 2008
MathSciNet review: 2415060
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09359-3
PII: S 0002-9939(08)09359-3
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.