Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Wednesday, April 09, 2008

Knot Monkey

Carl has been playing with knots that cover a sphere. Rather, when a piece of cord or wool is used, its substantial thickness allows a covering of a sphere with a small finite number of crossings.

In the mathematical world, ideal knots are drawn with an infinitely thin line. Such lines can still fill a sphere (a la Thurston) but monkey knot curves with crossings are more interesting in the context of M theoretic quantum information, and it would take some (kind of) infinite number of crossings to properly fill out a sphere. But basically, the monkey knot is a set of Borromean rings in three dimensions (or Borromean ribbons). The rings form a 6 crossing planar diagram. Note that if the outer 3 crossings are smoothed, one obtains a trefoil knot from the centre of the rings (along with a separate unknotted loop). I can't help wondering what this means.


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