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Mathematics

Fiber Bundles and the Hopf Fibration

Quick fact

The Hopf fibration describes how a circle (S¹) can be arranged around every point of a sphere (S²) so that the union forms a 3-dimensional sphere (S³) — yet this 3-sphere is not the simple product of the two spaces.

Why this is interesting

Imagine you have a rope wound around a stick: the rope looks like a cylinder, but if you twist it just right, the whole structure changes. What if a simple product space could secretly be a twisted bundle?

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Fiber Bundles and the Hopf Fibration

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