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
Encyclopedic overview
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.
Excerpted from Wikipedia’s “orbifold” article, available under the CC BY-SA 4.0 licence.