Hopf Fibration
S³ → S² — every circle links every other circle exactly once
Number of fibers
24
Rotation speed
0.5
Base point latitude
30
°
Stereo projection W
0.0
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Hopf fibration
η: S³ → S² maps the 3-sphere to the 2-sphere.
Each fiber η⁻¹(p) is a great circle on S³. The fibers are
pairwise linked
— any two Hopf circles link exactly once.
Visualized via
stereographic projection
S³ → ℝ³. Each S² base point (latitude, longitude) generates one colored circle fiber.
Drag to rotate. This fibration is the generator of π₃(S²) ≅ ℤ.
Color mode
By latitude
By longitude
Rainbow