Hopf fibration



The Hopf fibration may refer to one of various related mathematical structures. Most commonly, it refers to a symmetric partition of a 3-sphere into great circles. However, it may also refer to similar partitions of higher-dimensional hyperspheres by other spheres.

The Hopf fibrations are most often studied in topology as an example of a fiber bundle. However, they're also interesting from a geometric point of view as they give rise to many non-trivial symmetry groups. The usual Hopf fibration in particular is intricately related to the swirlchora and polytwisters, which can be thought of as "discrete" versions of it.