Geodesic
Surgery untying of coloured knots
Moskovich, Daniel1
1Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 673-697
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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.

DOI : 10.2140/agt.2006.6.673
Keywords: dihedral covering, covering space, Fox colouring, tricoloured knots, surgery presentation

Moskovich, Daniel  1

1 Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan 
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Moskovich, Daniel. Surgery untying of coloured knots. Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 673-697. doi: 10.2140/agt.2006.6.673

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