A. Rainer, Fakultat fur Mathematik, Universitat Wien, Nordbergstrasse 15, A-1090 Wien, Austria, e-mail: armin.rainer@univie.ac.at
Abstract: 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.
Keywords: orbit projection, proper $G$-manifold, fibration, quasifibration
Classification (MSC 2000): 55R05, 55R65, 57S15
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