Fundamental groups of topological stacks with slice property

Behrang Noohi

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 formulas for the fundamental group of the coarse quotient of a group action on a topological space in terms of the fixed point data. In particular, we recover, and vastly generalize, results of [Ar1, Ar2, Ba, Hi, Rh].