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

Brian Bollen, University at Albany, State University of New York


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.