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arXiv · 1203.4869

Microlocal Euler classes and Hochschild homology

Masaki Kashiwara·Pierre Schapira
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Abstract

We define the notion of a trace kernel on a manifold M. Roughly speaking, it is a sheaf on M x M for which the formalism of Hochschild homology applies. We associate a microlocal Euler class to such a kernel, a cohomology class with values in the relative dualizing complex of the cotangent bundle over M and we prove that this class is functorial with respect to the composition of kernels. This generalizes, unifies and simplifies various results of (relative) index theorems for constructible sheaves, D-modules and elliptic pairs.

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Masaki Kashiwara, Pierre Schapira. 2013-05-01. Microlocal Euler classes and Hochschild homology. https://doi.org/10.1017/s1474748013000169

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