Projective Dirac Operators, Twisted K-Theory, and Local Index Formula | Posted on:2012-06-17 | Degree:Ph.D | Type:Dissertation | University:California Institute of Technology | Candidate:Zhang, Dapeng | Full Text:PDF | GTID:1460390011968008 | Subject:Applied Mathematics | Abstract/Summary: | | 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. | Keywords/Search Tags: | Spectral triple, Projective, Manifold, Twisted | | Related items |
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