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Projective Dirac Operators, Twisted K-Theory, and Local Index Formula


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.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Twisted K-theory; spectral triple; Chern character
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Marcolli, Matilde
Thesis Committee:
  • Marcolli, Matilde (chair)
  • Agarwala, Susama
  • Calegari, Danny C.
  • Kitaev, Alexei
Defense Date:25 May 2011
Record Number:CaltechTHESIS:05272011-153933399
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6466
Deposited By: Dapeng Zhang
Deposited On:31 May 2011 21:36
Last Modified:28 Oct 2021 19:03

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