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Abstract
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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.
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Keywords
topological stack, fundamental group, Galois theory,
covering stack, slice property, coarse quotient, coarse
moduli
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Mathematical Subject Classification 2000
Primary: 54H15, 22A22, 22F05
Secondary: 57S30, 57S20, 57S10, 57S05
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Publication
Received: 11 January 2008
Revised: 14 June 2008
Accepted: 15 June 2008
Published: 8 August 2008
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