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Doubly Hopf fibred tori

Doubly Hopf fibred tori

C021/3709

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61.8 MB (1.6 MB compressed)

4800 x 4500 pixels

40.6 x 38.1 cm ⏐ 16.0 x 15.0 in (300dpi)

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Credit

PASIEKA / SCIENCE PHOTO LIBRARY PASIEKA / SCIENCE PHOTO LIBRARY

Caption

Doubly Hopf fibred tori. 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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