Does anybody here know some good resources or explanations of Hopf fibration and knots with GA?
You could start with my recent paper on Villarceau Rotors, which contains a full description of the Hopf fibration, and links to an earlier paper on knots.
Leo Dorst
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Definitely read @LeoDorst papers and related links (pun intended), especially his "3D conformal motions " and “Square Roots” papers.
Here also is a video of some knots wound around transforming hopf links I made with CGA
https://vimeo.com/62755547. A potentially useful description of how this works can be found on page 131 of my thesis (http://versor.mat.ucsb.edu/ArticulatingSpace.pdf), where I discuss a way to make a Hopf Fibration by finding the transformation that takes a Circle to its own Axis. Interestingly, polar Hopf links are orthogonal and commuting and so the (dual of) two hopf linked circles can be considered well-chosen (orthogonal and commuting) planes (e.g. commuting bivectors) around which one can weave a knot Ă la Dorst.
Also, I always found this article on Lorenz and Modular flows fascinating but beyond my understanding: http://www.josleys.com/articles/ams_article/Lorenz3.htm If I understand what you are up to @chakravala, you would probably get this modular flow stuff better than I do. Would love to see a GA explanation of this.
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That’s correct @wolftype the modular flows are a central aspect of my own research directions. Thanks for sharing the links, I am working towards making some future contributions in this area.