2 2 N ov 2 01 2 Projective Dirac operators , twisted K - theory , and local index formula ∗
نویسنده
چکیده
We construct a canonical noncommutative spectral triple for every oriented closed Riemannian manifold, which represents the fundamental class in the twisted K-homology of the manifold. This so-called “projective spectral triple” is Morita equivalent to the well-known commutative spin spectral triple provided that the manifold is spin-c. We give an explicit local formula for the twisted Chern character for K-theories twisted with torsion classes, and with this formula we show that the twisted Chern character of the projective spectral triple is identical to the Poincaré dual of the A-hat genus of the manifold. Mathematics Subject Classification (2010). 19K56, 19L50, 58J20.
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