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

Craig J. Sutton | Zendy

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

Author(s) -

Craig J. Sutton

Publication year - 2002

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/pl00012438

Subject(s) - isospectral , mathematics , conjugacy class , rigidity (electromagnetism) , homogeneous , pure mathematics , lattice (music) , group (periodic table) , simply connected space , isometric exercise , combinatorics , physics , medicine , quantum mechanics , acoustics , physical therapy

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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