Microlocal Lefschetz classes of graph trace kernels

TL;DR

This paper introduces graph trace kernels and their microlocal Lefschetz classes, establishing their functoriality and applying them to fixed point formulas for constructible sheaves.

Contribution

It generalizes trace kernels to graph trace kernels and proves the functoriality of their microlocal Lefschetz classes, with applications to fixed point formulas.

Findings

Defined graph trace kernels as a generalization of trace kernels

Proved functoriality of microlocal Lefschetz classes under composition

Applied to microlocal Lefschetz fixed point formula for constructible sheaves

Abstract

In this paper, we define the notion of graph trace kernels as a generalization of trace kernels. We associate a microlocal Lefschetz class with a graph trace kernel and prove that this class is functorial with respect to the composition of kernels. We apply graph trace kernels to the microlocal Lefschetz fixed point formula for constructible sheaves.