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Hopf Links

The family of tori depicted in Pendulum Tori is the basis for the Hopf fibration of the three-sphere by linked circles. The 1-1 curves on any of these tori are linked. Moreover, the 1-1 curves on any two of these tori also are linked. The collection of these 1-1 curves form the Hopf fibration.

Here we see a torus (one near the center of one of the solid tori) projected into three space as a small red torus. Another torus near the center of the other solid torus is projected to a large green torus (it provides the green background and the slender pillar down the middle). The blue bands represent several 1-1 bands on an intermediate torus. Note that they are linked with each other, as well as with the red and green tori.

This image appeared in Beyond the Third Dimension.

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Created: 13 Oct 2003
Last modified: Oct 13, 2003 5:58:26 PM
Comments to: dpvc@union.edu
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