Geodesic
Orbit projections as fibrations
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 2, pp. 529-538 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The orbit projection $\pi \: M \to M/G$ 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 $\pi $ is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: $\pi $ is a $G$-quasifibration if and only if all points are regular.
The orbit projection $\pi \: M \to M/G$ 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 $\pi $ is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: $\pi $ is a $G$-quasifibration if and only if all points are regular.
Classification : 55R05, 55R65, 57S15
Keywords: orbit projection; proper $G$-manifold; fibration; quasifibration 
@article{CMJ_2009_59_2_a15,
     author = {Rainer, Armin},
     title = {Orbit projections as fibrations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {529--538},
     year = {2009},
     volume = {59},
     number = {2},
     mrnumber = {2532388},
     zbl = {1224.55003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_2_a15/}
}
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Rainer, Armin. Orbit projections as fibrations. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 2, pp. 529-538. http://geodesic.mathdoc.fr/item/CMJ_2009_59_2_a15/