Fundamental groups of topological stacks with slice property

TL;DR

This paper derives a formula for the fundamental group of the coarse moduli space of a topological stack and applies it to group actions, generalizing classical results in the field.

Contribution

It introduces new formulas for the fundamental group of coarse quotients of group actions on topological spaces, extending previous work.

Findings

New formulas for fundamental groups of coarse quotients

Generalization of Armstrong, Bass, Higgins, Rhodes results

Simplified computation methods for topological stacks

Abstract

The main result of the paper is a formula for the fundamental group of the coarse moduli space of a topological stack. As an application, we find simple general formulas for the fundamental group of the coarse quotient of a group action on a topological space in terms of the fixed point data. The formulas seem, surprisingly, to be new. In particular, we recover, and vastly generalize, results of Armstrong, Bass, Higgins, Rhodes.