TFBCON2003 (Art/B3D)

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.

TFBCON2003 Web Pages Created: 13 Oct 2003 Last modified: Oct 13, 2003 5:58:26 PM Comments to: dpvc@union.edu

Figure-8 Klein Bottle Tom Banchoff's Mathematical Artwork Pendulum Tori