# Characteristic Cycles and the Relative Local Euler Obstruction

## TL;DR

This paper explores the local and relative local Euler obstructions using constructible sheaves, characteristic cycles, and vanishing cycles, providing a sheaf-theoretic approach to understanding these invariants in complex analytic spaces.

## Contribution

It introduces a new perspective on Euler obstructions through characteristic complexes and cycles, linking sheaf theory with singularity invariants.

## Key findings

- Characterizes local Euler obstruction via constructible complexes.
- Defines the relative local Euler obstruction using characteristic cycles.
- Connects sheaf-theoretic methods with classical invariants.

## Abstract

In this paper, we investigate the local Euler obstruction and the relative local Euler obstruction in terms of constructible complexes of sheaves, characteristic cycles, and vanishing cycles. The fundamental tool that we use is the notion of a characteristic complex for an analytic space embedded in affine space.