nLab
orbispace

Idea

An orbispace is a space, particularly a topological stack, that is locally modeled on the homotopy quotient/action groupoid of a locally compact topological space by a rigid group action.

Orbispaces are to topological spaces what orbifolds are to manifolds.

References

A detailed but elementary approach via atlases can be found in

• Weimin Chen, A homotopy theory of orbispaces (arXiv:math/0102020)

and another approach is sketched in

• André Henriques, Orbispaces and orbifolds from the point of view of the Borel construction, a new definition (arXiv:0112006)

• André Henriques, Vector bundles on orbispaces (2005) (pdf)