Equivariant isospectrality and Sunada's Method

2006/08/22 by Craig J. Sutton, Sutton, Craig J.
Mathematics · #53C20 #58J50 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Spectral Theory (math.SP) #math.DG #math.SP #msc:53C20 #msc:58J50

paper · pdf · doi:10.48550/arxiv.math/0608557

9 pages, shortened and rewritten with a new title and abstract, slight change in emphasis, to appear in Arch. Math. (Basel), published online June 5, 2010

openalex publication_date 2006/08/22 · arxiv created 2010/07/08 · arxiv updated 2010/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 O and a smooth manifold M are isospectral, then they cannot admit non-trivial finite Riemannian covers M₁ → O and M₂ → M where M₁ and M₂ are isospectral manifolds.

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