Fundamental groups of topological stacks with the slice property

Noohi, Behrang

doi:10.2140/agt.2008.8.1333

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Fundamental groups of topological stacks with the slice property

Behrang Noohi

Algebraic & Geometric Topology 8 (2008) 1333–1370

DOI: 10.2140/agt.2008.8.1333

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/

Volume 8, issue 3 (2008)