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The G-invariant spectrum and non-orbifold singularities. (English) Zbl 1379.58012

Summary: We consider the \(G\)-invariant spectrum of the Laplacian on an orbit space \(M/G\) where \(M\) is a compact Riemannian manifold and \(G\) acts by isometries. We generalize the Sunada-Pesce-Sutton technique to the \(G\)-invariant setting to produce pairs of isospectral non-isometric orbit spaces. One of these spaces is isometric to an orbifold with constant sectional curvature whereas the other admits non-orbifold singularities and therefore has unbounded sectional curvature. We conclude that constant sectional curvature and the presence of non-orbifold singularities are inaudible to the \(G\)-invariant spectrum.

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
58J53 Isospectrality
22D99 Locally compact groups and their algebras
53C12 Foliations (differential geometric aspects)
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