Commentarii Mathematici Helvetici


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Volume 77, Issue 4, 2002, pp. 701–717
DOI: 10.1007/PL00012438

Published online: 2002-12-31

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

C. J. Sutton[1]

(1) University of Pennsylvania, Philadelphia, USA

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.

Keywords: Spectral geometry, Laplace operator, homogeneous spaces, group actions

Sutton C.: Isospectral simply-connected homogeneous spaces and the spectral rigidity of group actions. Comment. Math. Helv. 77 (2002), 701-717. doi: 10.1007/PL00012438