Abstract
We construct pairs and continuous families of isospectral yet locally non-isometric orbifolds via an equivariant version of Sunada’s method. We also observe that if a good orbifold \({\mathcal{O}}\) and a smooth manifold M are isospectral, then they cannot admit non-trivial finite Riemannian covers \({M_1 \to\mathcal{O}}\) and M 2 → M where M 1 and M 2 are isospectral manifolds.
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This work was partially supported by an NSF Postdoctoral Research Fellowship and NSF grant DMS 0605247.
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Sutton, C.J. Equivariant isospectrality and Sunada’s method. Arch. Math. 95, 75–85 (2010). https://doi.org/10.1007/s00013-010-0139-8
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DOI: https://doi.org/10.1007/s00013-010-0139-8