  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. We show that the new invariant plays the same role with
respect to the spectral invariant as the Cabibbo--Kobayashi--Maskawa mixing
matrix in the Standard Model plays with respect to the list of masses of the
quarks.
