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arXiv · 1207.5728

\Gamma-extensions of the spectrum of an orbifold

Carla Farsi·Emily Proctor·Christopher Seaton
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Abstract

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

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Carla Farsi, Emily Proctor, Christopher Seaton. 2012-07-24. \Gamma-extensions of the spectrum of an orbifold. https://doi.org/10.1090/s0002-9947-2013-06082-5

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