An equivariant version of the Euler obstruction

TL;DR

This paper develops an equivariant extension of the Euler obstruction for complex analytic varieties with finite group actions, linking it to the equivariant radial index and creating new invariants in the Burnside ring.

Contribution

It introduces an equivariant Euler obstruction for invariant 1-forms, expanding classical invariants to incorporate group symmetries and their relations.

Findings

Defines the equivariant Euler obstruction in the Burnside ring.

Relates the equivariant Euler obstruction to the equivariant radial index.

Establishes equivariant versions of local and global Euler obstructions.

Abstract

For a complex analytic variety with an action of a finite group and for an invariant 1-form on it, we give an equivariant version (with values in the Burnside ring of the group) of the local Euler obstruction of the 1-form and describe its relation with the equivariant radial index defined earlier. This leads to equivariant versions of the local Euler obstruction of a complex analytic space and of the global Euler obstruction.