%0 Journal Article
%T ¦£-extensions of the spectrum of an orbifold
%A Carla Farsi
%A Emily Proctor
%A Christopher Seaton
%J Mathematics
%D 2012
%I arXiv
%R 10.1090/S0002-9947-2013-06082-5
%X 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.
%U http://arxiv.org/abs/1207.5728v2