higher geometry / derived geometry
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An orbifold $\mathcal{X}$ is called good (Thurston 92, Ch. 13, Def. 13.2.3) or developable if it is isomorphic to a global quotient of a smooth manifold $M$ by the action of a discrete group $\flat G$ (not necessarily finite):
Otherwise $\mathcal{X}$ is called bad.
If $\mathcal{X}$ is even the global quotient of a smooth manifold by a finite group action one says that it is very good.
In the other direction, an orbifold that is the global quotient of a smooth manifold by some (compact) Lie group is called a presentable orbifold.
The notion of good orbifolds is due to Def. 13.2.3 in:
William Thurston: Three-dimensional geometry and topology, preliminary draft, University of Minnesota (1992) [1979: ark:/13960/t3714t34v, 1991: pdf, 2002: pdf, pdf]
the first three chapters of which are published in expanded form as:
William Thurston: The Geometry and Topology of Three-Manifolds, Princeton University Press (1997) [ISBN:9780691083049, Wikipedia page]
Further discussion:
Last revised on June 8, 2024 at 13:05:03. See the history of this page for a list of all contributions to it.