, Volume 95, Issue 1, pp 75-85
Date: 05 Jun 2010

Equivariant isospectrality and Sunada’s method

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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 2M where M 1 and M 2 are isospectral manifolds.

This work was partially supported by an NSF Postdoctoral Research Fellowship and NSF grant DMS 0605247.