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We introduce an invariant of Riemannian geometry which measures the relative position of two von Neumann algebras in Hilbert space, and which, when combined with the spectrum of the Dirac operator, gives a complete invariant of Riemannian geometry.
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R. Nicoara, A finiteness result for commuting squares of matrix algebras
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A. Connes, On the spectral characterization of manifolds
2088
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1995
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A. Chamseddine, A. Connes, M. Marcolli, Gravity and the standard model with neutrino mixing
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A. Rennie, J.C. Varilly, Reconstruction of manifolds in noncommutative geometry
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J. Sylvester, On the reduction of a bilinear quantic of the n n ’th order to the form of a sum of n n products by a double orthogonal substitution
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2092
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