Mapping stacks of topological stacks

Details Mapping stacks of topological stacks Mapping stacks of topological stacks

2008-09-13

arxiv.org/abs/0809.2373v2

Mathematics

Algebraic Topology

16 pages

Scientific paper

We prove that the mapping stack Map(Y,X) of topological stacks X and Y is again a topological stack if Y admits a compact groupoid presentation. If Y admits a locally compact groupoid presentation, we show that Map(Y,X) is a paratopological stack. In particular, it has a classifying space (hence, a natural weak homotopy type). We prove an invariance theorem which shows that the weak homotopy type of the mapping stack Map(Y,X) does not change if we replace X by its classifying space, provided that Y is paracompact topological space. As an example, we describe the loop stack of the classifying stack BG of a topological group G in terms of twisted loop groups of G.

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