Hopf Stabilization
Here are a few pictures suggesting the change a Hopf stabilization makes to a fibered knot. Thought I’d share.
Basically I took 10 fibers, sliced them at angle, and made half of the slice translucent. It gives a glimpse of the dynamics involved.
Of course I had to play around with the colorings and renderings.
Rendering with glass looks neat, but it kinda distorts the innards a bit much.
There are a few more on the Flickr account. Just click on any of the above pictures to go there.
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.
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.
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.
Are those lines through the stabilized fibration reflective of rheotomic force lines?