Visualizing Seven-Manifolds

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A visualization of seven-manifolds based on Milnor's construction of exotic seven-spheres.

For more information, see
  1. Niles Johnson
  2. Milnor
  3. sphere
  4. seven-manifold
  5. exotic sphere
  6. 3D
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Комментарии
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Thanks for the upload. I came for the pictures, didn't understand anything else.

farazars
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thank you. I will share this with my middle schoolers

patrickleahey
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Wonderful rendering! The miracle shape is the simple trefoil knot where at any point the three circular strands are 90deg to each other. Just like EM.

Though the cardioid and its rotation are best model for our manifold imho.

KaliFissure
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"fibered over" refers to fiber bundle structure -- looks like a product in small regions. In this case these manifolds fit in fiber bundles where the base space is the 4-sphere and the fibers are 3-spheres.

NilesJohnson
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Interesting. Looks similar to the way I see life choices and patterns interlocking.

timenixe
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I didn't get it. Was it a projection on 3D (a slice) or something more advanced?

samtux
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If you want to jump to the end of the slides, go to 3:10

NilesJohnson
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Wish I was smart enough to understand this but for now I like the loopy loops

munda_music
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I would love to see this on 3-d computer game.

patrickleahey