Microlocal Euler classes and Hochschild homology
Algebraic Geometry
2014-06-04 v4
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.
Cite
@article{arxiv.1203.4869,
title = {Microlocal Euler classes and Hochschild homology},
author = {Masaki Kashiwara and Pierre Schapira},
journal= {arXiv preprint arXiv:1203.4869},
year = {2014}
}
Comments
The proof of Theorem 4.6 has been considerably simplified. To appear in the Journal of the Institute of Mathematics of Jussieu