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. doi:10.7907/B2Z4-P206. https://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 Poincare dual of the A-hat genus of the manifold.

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