Homotopy types of topological stacks

Details Homotopy types of topological stacks Homotopy types of topological stacks

2008-08-27

arxiv.org/abs/0808.3799v2

Mathematics

Algebraic Topology

33 pages

Scientific paper

We define the notion of {\em classifying space} of a topological stack and show that every topological stack \X has a classifying space X which is a topological space well-defined up to weak homotopy equivalence. Under a certain paracompactness condition on \X, we show that X is actually well-defined up to homotopy equivalence. These results are formulated in terms of functors from the category of topological stacks to the (weak) homotopy category of topological spaces. We prove similar results for (small) diagrams of topological stacks.

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