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good orbifold

Contents

Context

Geometry

Higher Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Contents

Definition

An orbifold 𝒳\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 MM by the action of a discrete group G\flat G (not necessarily finite):

𝒳MG \mathcal{X} \,\simeq\, M \sslash \flat G

Otherwise 𝒳\mathcal{X} is called bad.

If 𝒳\mathcal{X} is even the global quotient of a finite group one also says that it is very good.

References

  • William Thurston, Three-dimensional geometry and topology, preliminary draft, University of Minnesota, Minnesota, (1992)

    which in completed and revised form is available as his book:

    The Geometry and Topology of Three-Manifolds; (web)

    in particular the orbifold discussion is in chapter 13

Last revised on June 19, 2021 at 12:41:28. See the history of this page for a list of all contributions to it.