Riemannian Geometries
نویسنده
چکیده
In this paper we provide a non-commutative version of the fundamental class [dM ] = [(L 2(M,Λ∗(T ∗M)), d+ d∗, ε)] of a smooth closed Riemannian manifold M . The formulation involves elements of A. Connes’ non-commutative geometry, G. Kasparov’s KK-theory and the standard theory of von Neumann algebras. Using axioms based on [C1], it is proved we can recover the ordinary differential geometry of closed Riemannian manifolds in this non-commutative generalisation.
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