Algebraic & Geometric Topology

Fundamental groups of topological stacks with the slice property

Behrang Noohi

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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 Armstrong, Bass, Higgins and Taylor and Rhodes.

Article information

Algebr. Geom. Topol., Volume 8, Number 3 (2008), 1333-1370.

Received: 11 January 2008
Revised: 14 June 2008
Accepted: 15 June 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54H15: Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx] 22A22: Topological groupoids (including differentiable and Lie groupoids) [See also 58H05] 22F05: General theory of group and pseudogroup actions {For topological properties of spaces with an action, see 57S20}
Secondary: 57S30: Discontinuous groups of transformations 57S20: Noncompact Lie groups of transformations 57S10: Compact groups of homeomorphisms 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms

topological stack fundamental group Galois theory covering stack slice property coarse quotient coarse moduli


Noohi, Behrang. Fundamental groups of topological stacks with the slice property. Algebr. Geom. Topol. 8 (2008), no. 3, 1333--1370. doi:10.2140/agt.2008.8.1333.

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