Microlocal study of Lefschetz fixed point formulas for higher-dimensional fixed point sets

TL;DR

This paper develops a microlocal geometric framework using Lagrangian cycles to analyze Lefschetz fixed point formulas for fixed point sets of higher dimension, enhancing understanding of local contributions.

Contribution

Introduces new Lagrangian cycles that encode local Lefschetz contributions and studies their functorial properties for higher-dimensional fixed point sets.

Findings

Lagrangian cycles effectively encode local Lefschetz contributions

Functorial properties facilitate geometric analysis of fixed point formulas

Application to higher-dimensional fixed point sets broadens the scope of Lefschetz theory

Abstract

We introduce new Lagrangian cycles which encode local contributions of Lefschetz numbers of constructible sheaves into geometric objects. We study their functorial properties and apply them to Lefschetz fixed point formulas with higher-dimensional fixed point sets.