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Irrational Eigenvalues of the Discrete Laplacian: A Study of Simplical Complexes

2017
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Thesis / Dissertation Description

We study the behavior of eigenvalues of the discrete Laplacian of an abstract simplicial complex K when subdividing a single face of K . We show that if K is a simplex, performing this kind of restricted subdivision twice on a single face produces irrational eigenvalues for the discrete Laplacian.

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