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arXiv · 1607.05593

The G-invariant spectrum and non-orbifold singularities

Ian M. Adelstein·Mary R. Sandoval
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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 therefore show that constant sectional curvature and the presence of non-orbifold singularities are inaudible to the G-invariant spectrum.

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Ian M. Adelstein, Mary R. Sandoval. 2016-07-19. The G-invariant spectrum and non-orbifold singularities. https://arxiv.org/abs/1607.05593

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