Orbit projections as fibrations

The orbit projection $π: M \to M/G$ of a proper $G$-manifold $M$ is a fibration if and only if all points in $M$ are regular. Under additional assumptions we show that $π$ is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: $π$ is a $G$-quasifibration if and only if all points are regular.

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