Projective Dirac operators, twisted K-theory, and local index formula

Citation

Zhang, Dapeng (2011) Projective Dirac operators, twisted K-theory, and local index formula. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05272011-153933399

Abstract

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 Poincar\'e dual of the A-hat genus of the manifold.

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