G-category versus orbifold category

TL;DR

This paper compares invariants of group actions and orbifolds, showing that Fadell's equivariant category matches the Lusternik-Schnirelmann category for orbifolds when the group is finite.

Contribution

It establishes the equivalence of Fadell's equivariant category and the orbifold Lusternik-Schnirelmann category for finite groups.

Findings

Fadell's equivariant category equals orbifold LS category for finite groups

Provides a bridge between group action invariants and orbifold invariants

Enhances understanding of orbifold topology in relation to group actions

Abstract

We present a comparative study of certain invariants defined for group actions and their analogues defined for orbifolds. In particular, we prove that Fadell's equivariant category for $G$-spaces coincides with the Lusternik-Schnirelmann category for orbifolds when the group is finite.