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July 2, 2016

separation of the joining

Filed under: knot idea outline — Rob @ 1:06 pm

IMG_20160702_0003To look for one of these new moves, consider the joining (e(3,2)*e(3,1)). These e’s do not represent specific parts, but these represent what were crossings in the original knot diagram. That means when sections of the curves move in the plane, under movement of the e’s without the coincident p’s. the e’s move with the joining, they do not separate unless we want them too.

But now since the joining is made up of two parts I can freeze the diagram and separate them with the coincident p’s  along the two different curves leaving an joining of two parts which do not join in the original diagram-see bottom diagram.

 

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