Approximation of spectra results for twisted Laplace operators
by Zahariev, Svetoslav, Ph.D., CITY UNIVERSITY OF NEW YORK, 2007, 61 pages; 3283185

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. We also show how to extend the construction of discrete magnetic Laplace operators on graphs [32] to simplicial complexes.

 
AdviserJozef Dodziuk
SchoolCITY UNIVERSITY OF NEW YORK
SourceDAI/B 68-09, p. , Jan 2008
Source TypeDissertation
SubjectsMathematics
Publication Number3283185
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