Homotopy types of topological stacks

2008/08/27 by Behrang Noohi, Noohi, Behrang
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT

paper · pdf · doi:10.48550/arxiv.0808.3799

33 pages

arxiv created 2010/04/30 · arxiv updated 2010/05/04

Abstract

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.

Related

• Mapping stacks of topological stacks
• The homotopy type of a topological stack
• Homotopy types of topological stacks of categories
• Foundations of Topological Stacks I
• Homotopy homomorphisms and the classifying space functor