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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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$\Gamma$-extensions of the spectrum of an orbifold
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by Carla Farsi, Emily Proctor and Christopher Seaton PDF
Trans. Amer. Math. Soc. 366 (2014), 3881-3905 Request permission


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, in 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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Additional Information
  • Carla Farsi
  • Affiliation: Department of Mathematics, University of Colorado at Boulder, Campus Box 395, Boulder, Colorado 80309-0395
  • MR Author ID: 311031
  • Email:
  • Emily Proctor
  • Affiliation: Department of Mathematics, Middlebury College, Middlebury, Vermont 05753
  • Email:
  • Christopher Seaton
  • Affiliation: Department of Mathematics and Computer Science, Rhodes College, 2000 N. Parkway, Memphis, Tennessee 38112
  • MR Author ID: 788748
  • Email:
  • Received by editor(s): August 20, 2012
  • Received by editor(s) in revised form: December 12, 2012
  • Published electronically: December 27, 2013
  • © Copyright 2013 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3881-3905
  • MSC (2010): Primary 58J53, 57R18; Secondary 53C20
  • DOI:
  • MathSciNet review: 3192622