Wednesday, May 06, 2009

[iqyxqxdk] Knots and 4d

Here is something mind bending.

Closed loops can be knotted (knot theory) in 3D. If the analogy is correct, closed 2D surfaces can be knotted in four dimensions: sphere, torus, Klein bottle, etc. (I think the Klein bottle may be constructed without self intersecting surfaces in 4D. )

Even more mindbendingly, these knotted surfaces can be unknotted in five dimensions. Closed loops in 3D may be unknotted in 4D.

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