Hopf Fibration (Annuli III)

Hopf 8 right

When talking about tori, at some point the Hopf fibration will make its appearance.
It all begins with a few tori of revolution packed together. Think about circular wires
bundled into one thick cable.

Simple

Cut through all the wires, twist the cable by 360 degrees, and reconnect wires of equal color.

Twist

Now all wires are interlinked, and this has the advantage that you can extend all this wiring to all of space (except for the vertical axis) in an even way to het what mathematicians call a fibre bundle.

Side

One can increase the complexity by showing nested wires by removing parts of then. The top view below is a simplified version of the picture at the top.

Top

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