Hopf fibration
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In differential topology, the Hopf fibration describes a 3-sphere in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle. Te
Pairwise linked keyrings mimic part of the Hopf fibration.
Bloch sphere
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In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system, named after the physicist Felix Bloch.
Hopf fibration
…is not null-homotopic. In fact it generates the homotopy group π3(S2) and has infinite order. In quantum mechanics, the Riemann sphere is known as the Bloch sphere, and the Hopf fibration describes the topological structure of a quantum mechanical two-level system or qubit. Similarly, the topology of a pair of…
Riemann Spin 2States