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Surgery untying of coloured knots

Daniel Moskovich
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Abstract

For p=3 and for p=5 we prove that there are exactly p equivalence classes of p-coloured knots modulo (+/-1)--framed surgeries along unknots in the kernel of a p-colouring. These equivalence classes are represented by connect-sums of n left-hand (p,2)-torus knots with a given colouring when n=1,2,...,p. This gives a 3-colour and a 5-colour analogue of the surgery presentation of a knot.

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Daniel Moskovich. 2009-04-06. Surgery untying of coloured knots. https://doi.org/10.2140/agt.2006.6.673

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