Surgery untying of coloured knots

Details Surgery untying of coloured knots Surgery untying of coloured knots

2005-06-27

arxiv.org/abs/math/0506541v6

Algebr. Geom. Topol. 6 (2006) 673-697

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 24 May 2006

Scientific paper

10.2140/agt.2006.6.673

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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