-extensions of the spectrum of an orbifold
Abstract
We introduce the -extension of the spectrum of the Laplacian of a Riemannian orbifold, where is a finitely generated discrete group. This extension, called the -spectrum, is the union of the Laplace spectra of the -sectors of the orbifold, and hence constitutes a Riemannian invariant that is directly related to the singular set of the orbifold. We compare the -spectra of known examples of isospectral pairs and families of orbifolds and demonstrate that it many cases, isospectral orbifolds need not be -isospectral. We additionally prove a version of Sunada's theorem that allows us to construct pairs of orbifolds that are -isospectral for any choice of .
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