Hopf Stabilization

Here are a few pictures suggesting the change a Hopf stabilization makes to a fibered knot. Thought I’d share.

Picture 7

Basically I took 10 fibers, sliced them at angle, and made half of the slice translucent. It gives a glimpse of the dynamics involved.

Picture 5

Picture 9

Of course I had to play around with the colorings and renderings.

Picture 12

Picture 26

Rendering with glass looks neat, but it kinda distorts the innards a bit much.

Picture 25

There are a few more on the Flickr account. Just click on any of the above pictures to go there.

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~ by Ken Baker on January 23, 2010.

5 Responses to “Hopf Stabilization”

  1. Simply wonderful renderings…I can’t quite appreciate the math behind them, as I’m still a beginner in topology, only now getting down the fundamentals of homotopy and the fundamental group. Your blog is inspiring.

  2. Beautiful visually and mathematically. Once again, I posted a link and thumbnail on my facebook page for my 640 “friends” — many in Math, Science, or Art.

  3. Wow! Is this created with SketchUp?

    • lol, no. It was created with Rhino3D. Dunno how you’d get the materials right in Sketchup. The model itself, however, could be reasonably created in Sketchup… though it would take a few tricks to get the surfaces looking right.

  4. Are those lines through the stabilized fibration reflective of rheotomic force lines?

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