Contents

# Contents

## Definition

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):

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

Otherwise $\mathcal{X}$ is called bad.

If $\mathcal{X}$ 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.