Dirac index classes and the noncommutative spectral flow

@inproceedings{Leichtnam2003DiracIC,
  title={Dirac index classes and the noncommutative spectral flow},
  author={Eric Leichtnam and Paolo Piazza},
  year={2003}
}
We present a detailed proof of the existence-theorem for noncommutative spectral sections (see the noncommutative spectral flow, unpublished preprint, 1997). We apply this result to various index-theoretic situations, extending to the noncommutative context results of Booss–Wojciechowski, Melrose–Piazza and Dai–Zhang. In particular, we prove a variational formula, in K∗(Cr∗(Γ)), for the index classes associated to 1-parameter family of Dirac operators on a Γ-covering with boundary; this formula… CONTINUE READING
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