Mapping stacks of topological stacks
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 September 2008
 DOI:
 10.48550/arXiv.0809.2373
 arXiv:
 arXiv:0809.2373
 Bibcode:
 2008arXiv0809.2373N
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Algebraic Geometry
 EPrint:
 16 pages