About

In the mathematical field of topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a $3$-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle. Technically, Hopf found a many-to-one continuous function (or "map") from the $3$-sphere onto the $2$-sphere such that each distinct point of the $2$-sphere comes from a distinct circle of the $3$-sphere (Hopf 1931). Thus the $3$-sphere is composed of fibers, where each fiber is a circle — one for each point of the $2$-sphere.

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