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Microlocal Euler classes and Hochschild homology

  • Masaki Kashiwara (a1) (a2) and Pierre Schapira (a3) (a4)

Abstract

We define the notion of a trace kernel on a manifold $M$ . Roughly speaking, it is a sheaf on $M\times M$ for which the formalism of Hochschild homology applies. We associate a microlocal Euler class with such a kernel, a cohomology class with values in the relative dualizing complex of the cotangent bundle ${T}^{\ast } M$ over $M$ , and we prove that this class is functorial with respect to the composition of kernels.

This generalizes, unifies and simplifies various results from (relative) index theorems for constructible sheaves, $\mathscr{D}$ -modules and elliptic pairs.

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References

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Microlocal Euler classes and Hochschild homology

  • Masaki Kashiwara (a1) (a2) and Pierre Schapira (a3) (a4)

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