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Orbit projections as fibrations

Armin Rainer (2009)

Czechoslovak Mathematical Journal

The orbit projection π M 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.

Orbit projections of proper Lie groupoids as fibrations

Armin Rainer (2009)

Czechoslovak Mathematical Journal

Let 𝒢 M be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection M M / 𝒢 is a fibration if and only if 𝒢 M is regular.

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