Homotopy types of topological stacks
By B. Noohi. 2008
60 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0c0185cf235a9f8cc89c1ba3928b4d384b99fef9
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the structure of instability in moduli theory (2014, methodology): “a groupoid in schemes and then taking the analytification, which is a groupoid in topological spaces. The cohomology is then defined as the cohomology of the classifying space of this topological stack [N2]. For global quotient stacks X= X/Gthis agrees with the equivariant cohomology H∗ Gan(X an) whic”
- Local Systems on Proper Algebraic V -manifolds (2010, background): “This brings us back to Noohi’s construction of the topological realization of a stack [79], and similar constructions considered by Gepner, Henriques [44] and Ebert [40].”