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Reconstruction of manifolds in noncommutative geometry
(2008-01-31)
We show that the algebra A of a commutative unital spectral triple (A,H,D) satisfying several additional conditions, slightly stronger than those proposed by Connes, is the algebra of smooth functions on a compact spin manifold.
Orbifolds are not commutative geometries
(2008)
In this note we show that the crucial orientation condition for commutative geometries fails for the natural commutative spectral triple of an orbifold M/G.
Riemannian manifolds in noncommutative geometry
(2012-07)
We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c manifolds; and conversely, ...