THE HOMOLOGY OF ALGEBRAS OF PSEUDO-DIFFERENTIAL SYMBOLS AND THE NON-COMMUTATIVE RESIDUE

@inproceedings{Brylinski2002THEHO,
  title={THE HOMOLOGY OF ALGEBRAS OF PSEUDO-DIFFERENTIAL SYMBOLS AND THE NON-COMMUTATIVE RESIDUE},
  author={Jean-Luc Brylinski and Ezra Getzler},
  year={2002}
}
We will perform the calculation by two completely different methods, each of which has some advantages. In the first, we filter the algebra in question as in [2], and use a homogeneity argument to show that the resulting spectral sequence degenerates. From this point of view, the homology is seen to be a “semi-classical” invariant, since it is calculated at first order in Planck’s constant, as the homology of the differential forms on T ∗M with respect to the operator δ : Ω∗(T ∗M) → Ω∗−1(T ∗M… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 13 references

Hyperfunctions and pseudo-differential equations, Lecture

  • M. Sato, M. Kashiwara, T. Kawai
  • Notes in Mathematics,
  • 1973
Highly Influential
6 Excerpts

A differential complex for Poisson manifolds, IHES

  • J. L. Brylinski
  • 1986
Highly Influential
8 Excerpts

A new proof of Weyl’s formula on the asymptotic distribution of eigenvalues

  • V. Guillemin
  • Adv. Math
  • 1985
Highly Influential
7 Excerpts

Cyclic homology and the Lie algebra homology of matrices

  • J. L. Loday, D. Quillen
  • Comment. Math. Helv
  • 1984
Highly Influential
5 Excerpts

Some examples of Hochschild and cyclic cohomology, Brown preprint

  • J. L. Brylinski
  • 1986
1 Excerpt

Local invariants of spectral assymetry

  • M. Wodzicki
  • Invent. Math
  • 1984
2 Excerpts

Systems of microdifferential equations

  • M. Kashiwara
  • Progress in Math.,
  • 1983
2 Excerpts

On holonomic systems of microdifferential equations, III—Systems with regular singularities, Publ

  • M. Kashiwara, T. Kawai
  • RIMS, Kyoto Univ
  • 1981
1 Excerpt

Deformations of Poisson brackets , Harmonic analysis and representations of Lie groups

  • Feigin, P. Tsygan
  • 1980