How to untie a trefoil knot?
August 30, 2011 10:58 PM Subscribe
Mathematics/Topology: how to untie a trefoil knot in four dimensions?
posted by knz to science & nature (10 answers total) 3 users marked this as a favorite
To my general understanding all 3d knots are not really knots four dimensions; practically I thought this simply involved looking at the process of tying the knot over time, and observing that the process is reversible -- that there is thus no point in 4d at which the simple string "unknot" is fundamentally changed to a knot.
However when I looked at the trefoil knot
this understanding fell to pieces. Obviously there is no process to build a trefoil that starts from an untied string without changing its topology fundamentally (by closing the ends together).
Hence my question: probably the trefoil knot is still no knot in 4d, but how so? Can you point me to any resource which helps visualizing the topology of a trefoil in 4d?