Isospectral simply-connected homogeneous spaces and the spectral rigidity of group actions

Details Isospectral simply-connected homogeneous spaces and the spectral rigidity of group actions Isospectral simply-connected homogeneous spaces and the spectral rigidity of group actions

2003-01-31

arxiv.org/abs/math/0301376v1

Comment. Math. Helv. 77 (2002) 701-717

Mathematics

Differential Geometry

16 pages. To appear in Commment. Math. Helv

Scientific paper

We generalize Sunada's method to produce new examples of closed, locally non-isometric manifolds which are isospectral. In particular, we produce pairs of isospectral, simply-connected, locally non-isometric normal homogeneous spaces. These pairs also allow us to see that in general group actions with discrete spectra are not determined up to measurable conjugacy by their spectra. In particular, we show this for lattice actions.

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