higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
$\infty$-Lie groupoids
$\infty$-Lie groups
$\infty$-Lie algebroids
$\infty$-Lie algebras
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 first three chapters are published in expanded form as
The book has its own Wikipedia page.
Last revised on October 26, 2022 at 23:21:56. See the history of this page for a list of all contributions to it.