A short proof of a formula of Brasselet, Le and Seade for the Euler obstruction

TL;DR

This paper provides a concise proof of a formula for the Euler obstruction using the index theorem for the vanishing cycle functor, simplifying previous approaches.

Contribution

It offers a shorter, more direct proof of the Euler obstruction formula by applying the index theorem for vanishing cycles.

Findings

Simplified proof of the Euler obstruction formula

Application of the index theorem for vanishing cycle functor

Enhanced understanding of the relationship between index theory and Euler obstruction

Abstract

Using the index theorem of Dubson, Le, Ginsburg and Sabbah for the vanishing cycle functor, we give a short proof of formula of Brasselet, Le and Seade for the Euler obstruction.