Equivariant indices of vector fields and 1-forms

TL;DR

This paper introduces equivariant versions of classical indices for vector fields and 1-forms on singular varieties with finite group actions, extending Poincaré-Hopf theorems to the equivariant setting.

Contribution

It defines equivariant radial and GSV-indices valued in the Burnside ring, and proves Poincaré-Hopf type theorems for these indices.

Findings

Defined equivariant indices with values in the Burnside ring.

Proved Poincaré-Hopf type theorems for the equivariant indices.

Described properties of the equivariant indices.

Abstract

Equivariant versions of the radial index and of the GSV-index of a vector field or a 1-form on a singular variety with an action of a finite group are defined. They have values in the Burnside ring of the group. Poincar\'e-Hopf type theorems for them are proven and some of their properties are described.