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)
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 â€Â\" one for each point of the 2-sphere."
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Keywords: -dimensional, 3-sphere, bundle, circles, continuous, cut-, cut-outs, cutout, cutouts, doubly, fiber, fibration, fibred, function, heinz, homogeneous, hopf, hypersphere, map, principal, projection, space, stereographic, tori, torus, vector
