14: London Tsai - The Reclusive Dean of The New Escherians: Difference between revisions

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https://www.bookofproofs.org/graphics/portraits/Hopf.jpeg

[https://en.wikipedia.org/wiki/Heinz_Hopf Heinz Hopf] was a German mathematician who worked on the fields of topology and geometry.

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https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Hopf_Fibration.png/500px-Hopf_Fibration.png

In the mathematical field of differential topology, the [https://en.wikipedia.org/wiki/Hopf_fibration 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 is mapped to from a distinct great 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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