orbifold
Sign in to saveAlso known as orbit-manifold
alt=Hyperbolic symmetry comparison to Euclidean symmetry|thumb|23star Orbifold Example In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space that is locally a finite group quotient of a Euclidean space.
~51 min read
Article
28 sectionsContents
- Formal definitions
- Definition using orbifold atlas
- Definition using Lie groupoids
- Relation between the two definitions
- Examples
- Orbifold fundamental group
- Orbifolds as diffeologies
- Orbispaces
- Complexes of groups
- Definition
- Example
- Edge-path group
- Developable complexes
- Orbihedra
- Definition
- Main properties
- Triangles of groups
- Mumford's example
- Generalizations
- Two-dimensional orbifolds
- 3-dimensional orbifolds
- Applications
- Orbifolds in string theory
- Calabi–Yau manifolds
- Music theory
- See also
- Notes
- References
alt=Hyperbolic symmetry comparison to Euclidean symmetry|thumb|23star Orbifold Example In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space that is locally a finite group quotient of a Euclidean space.
Definitions of orbifold have been given several times: by Ichirō Satake in the context of automorphic forms in the 1950s under the name V-manifold; by William Thurston in the context of the geometry of 3-manifolds in the 1970s when he coined the name orbifold, after a vote by his students; and by André Haefliger in the 1980s in the context of Mikhail Gromov's programme on CAT(k) spaces under the name orbihedron.