Fibrations of topological stacks

Details Fibrations of topological stacks Fibrations of topological stacks

2010-10-08

arxiv.org/abs/1010.1748v1

Mathematics

Algebraic Topology

25 pages

Scientific paper

In this note we define fibrations of topological stacks and establish their main properties. We prove various standard results about fibrations (fiber homotopy exact sequence, Leray-Serre and Eilenberg-Moore spectral sequences, etc.). We prove various criteria for a morphism of topological stacks to be a fibration, and use these to produce examples of fibrations. We prove that every morphism of topological stacks factors through a fibration and construct the homotopy fiber of a morphism of topological stacks. When restricted to topological spaces our notion of fibration coincides with the classical one.

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