The homotopy type of a topological stack

Details The homotopy type of a topological stack The homotopy type of a topological stack

2009-01-21

arxiv.org/abs/0901.3295v1

Mathematics

Algebraic Topology

12 pages

Scientific paper

The notion of the \emph{homotopy type} of a topological stack has been around in the literature for some time. The basic idea is that an atlas $X \to \mathfrak{X}$ of a stack determines a topological groupoid $\mathbb{X}$ with object space $X$. The homotopy type of $\mathfrak{X}$ should be the classifying space $B \mathbb{X}$. The choice of an atlas is not part of the data of a stack and hence it is not immediately clear why this construction of a homotopy type is well-defined, let alone functorial. The purpose of this note is to give an elementary construction of such a homotopy-type functor.

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