Obstruction Theory in Fiber Spaces.
The orbit projection of a proper -manifold is a fibration if and only if all points in are regular. Under additional assumptions we show that is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: is a -quasifibration if and only if all points are regular.
Let be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection is a fibration if and only if is regular.