For and for we prove that there are exactly equivalence classes of –coloured knots modulo –framed surgeries along unknots in the kernel of a –colouring. These equivalence classes are represented by connect-sums of left-hand –torus knots with a given colouring when . This gives a –colour and a –colour analogue of the surgery presentation of a knot.
"Surgery untying of coloured knots." Algebr. Geom. Topol. 6 (2) 673 - 697, 2006. https://doi.org/10.2140/agt.2006.6.673