Noncommutative spectral geometry of Riemannian foliations: some results and open problems

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We review some applications of noncommutative geometry to the study of transverse geometry of Riemannian foliations and discuss open problems.
35 pages, final version, minor changes, to appear in Proceedings of the Conference "Foliations-2005" (Lodz, Poland), World Scientific, Singapore, 2006

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