Projective Dirac Operators, Twisted K-Theory and Local Index Formula
Differential Geometry
2014-07-01 v2 K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.1008.0707,
title = {Projective Dirac Operators, Twisted K-Theory and Local Index Formula},
author = {Dapeng Zhang},
journal= {arXiv preprint arXiv:1008.0707},
year = {2014}
}
Comments
Provides complete proofs to the main theorems, and corrected errors in version 1. Removed the section on Lie Algebroid