2013
DOI: 10.1090/s0002-9947-2013-06082-5
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$\Gamma $-extensions of the spectrum of an orbifold

Abstract: We introduce the Γ-extension of the spectrum of the Laplacian of a Riemannian orbifold, where Γ is a finitely generated discrete group. This extension, called the Γ-spectrum, is the union of the Laplace spectra of the Γ-sectors of the orbifold, and hence constitutes a Riemannian invariant that is directly related to the singular set of the orbifold. We compare the Γ-spectra of known examples of isospectral pairs and families of orbifolds and demonstrate that, in many cases, isospectral orbifolds need not be Γ-… Show more

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Cited by 3 publications
(1 citation statement)
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“…Specifically, the last author [Sta05] obtained an upper bound on the order of isotropy groups that can arise in elements of the set I k (d) (expanded to contain orbifolds), the last author and Emily Proctor [PS10] showed orbifold diffeomorphism finiteness for I k (2), Proctor [Pro12] obtained orbifold homeomorphism finiteness for I k (d) assuming only isolated singularities, and John Harvey [Har16] obtained orbifold homeomorphism finiteness for the full set I k (d). In addition, Farsi, Proctor and Christopher Seaton [FPS14] introduced and studied a stronger notion of isospectrality of orbifolds.…”
Section: Consequentlymentioning
confidence: 99%
“…Specifically, the last author [Sta05] obtained an upper bound on the order of isotropy groups that can arise in elements of the set I k (d) (expanded to contain orbifolds), the last author and Emily Proctor [PS10] showed orbifold diffeomorphism finiteness for I k (2), Proctor [Pro12] obtained orbifold homeomorphism finiteness for I k (d) assuming only isolated singularities, and John Harvey [Har16] obtained orbifold homeomorphism finiteness for the full set I k (d). In addition, Farsi, Proctor and Christopher Seaton [FPS14] introduced and studied a stronger notion of isospectrality of orbifolds.…”
Section: Consequentlymentioning
confidence: 99%