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The G-invariant spectrum and non-orbifold singularities

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Trinity College, Hartford, CT , 06106, USA

    Ian M. Adelstein & M. R. Sandoval

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  1. Ian M. Adelstein
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  2. M. R. Sandoval
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Correspondence to Ian M. Adelstein.

Additional information

The authors would like to thank Carolyn Gordon and David Webb for many helpful conversations, as well as Emilio Lauret for providing valuable feedback. We would like to acknowledge the support of the NSF, Grant DMS-1632786. Finally, we would like to thank the referee for his or her thorough, prompt, and helpful review of the paper.

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Adelstein, I.M., Sandoval, M.R. The G-invariant spectrum and non-orbifold singularities. Arch. Math. 109, 563–573 (2017). https://doi.org/10.1007/s00013-017-1089-1

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  • DOI: https://doi.org/10.1007/s00013-017-1089-1

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