Volume 8, issue 3 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Fundamental groups of topological stacks with the slice property

Behrang Noohi

Algebraic & Geometric Topology 8 (2008) 1333–1370
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 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.

Keywords
topological stack, fundamental group, Galois theory, covering stack, slice property, coarse quotient, coarse moduli
Mathematical Subject Classification 2000
Primary: 54H15, 22A22, 22F05
Secondary: 57S30, 57S20, 57S10, 57S05
References
Publication
Received: 11 January 2008
Revised: 14 June 2008
Accepted: 15 June 2008
Published: 8 August 2008
Authors
Behrang Noohi
Florida State University
Department of Mathematics
Tallahassee, Florida 32306-4510
USA
http://www.math.fsu.edu/~noohi/