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

2003/01/31 by Craig J. Sutton
Mathematics · #math.DG #math.SP #msc:58J50

paper · pdf

published as Comment. Math. Helv. 77 (2002) 701-717 · 16 pages. To appear in Commment. Math. Helv

arxiv created 2003/01/31 · arxiv updated 2009/11/30

Abstract

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.

Related

• Spectral rigidity of group actions on homogeneous spaces
• Isospectral manifolds with different local geometries
• Equivariant isospectrality and Sunada's Method
• Almost isometric actions, property (T), and local rigidity
• Characteristic free measure rigidity for the action of solvable groups on homogeneous spaces