The local index formula in noncommutative geometry revisited

@inproceedings{Carey2017TheLI,
  title={The local index formula in noncommutative geometry revisited},
  author={Alan L. Carey and John Phillips and Adam Rennie and Fedor Sukochev},
  year={2017}
}
In this review we discuss the local index formula in noncommutative geomety from the viewpoint of two new proofs are partly inspired by the approach of Higson especially that in but they differ in several fundamental aspedcts, in particular they apply to semifinite spectral triples for a *s-subalgebra A of a general semifinite von Neumann algebra. Our proofs are novel even in the setting of the original theorem and reduce the hypotheses of the theorem to those necessary for its statement. These… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 43 references

Spectral flow in type I and type II factors-a new approach

  • J. Phillips
  • Fields Institute Communications, 17
  • 1997
Highly Influential
5 Excerpts

The local index formula in noncommutative geometry

  • A. Connes, H. Moscovici
  • Geom. Funct. Anal., 5
  • 1995
Highly Influential
10 Excerpts

An index theorem for Toeplitz operators with noncommutative symbol space

  • J. Phillips, I. Raeburn
  • J. Funct. Anal., 120
  • 1993
Highly Influential
8 Excerpts

Quasi-homomorphismes

  • A. Connes, J. Cuntz
  • cohomologie cyclique et positivité, Commun. Math…
  • 1988
Highly Influential
4 Excerpts

Spectral flow in θ-summable Fredholm modules

  • A. L. Carey, J. Phillips
  • eta invariants and the JLO cocycle, K-Theory, 31
  • 2004
Highly Influential
5 Excerpts

Toeplitz operators on flows J

  • R. Curto, P. S. Muhly, J. Xia
  • Funct. Anal. 93
  • 1990
Highly Influential
10 Excerpts

Singer C∗-algebras of operators on a half space II: index theory

  • L. A. Coburn, R. G. Douglas, I.M.D.G. Schaeffer
  • IHES Publ. Math
  • 1971
Highly Influential
10 Excerpts

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