Homotopy types of topological stacks,

Behrang Noohi

We show that an arbitrary topological stack X has a natural weak homotopy type. Under a certain paracompactness condition on X, we show that X actually has a natural homotopy type. We also prove these results for diagrams of topological stacks. These results are formulated in terms of func- tors from the category of topological stacks to the (weak) homotopy category of topological spaces. We show how this can be used to extend (co)homology theories to topological stacks. We prove similar results for small diagrams of topological stacks.