#### Volume 6, issue 2 (2006)

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Surgery untying of coloured knots

### Daniel Moskovich

Algebraic & Geometric Topology 6 (2006) 673–697
 arXiv: math.GT/0506541
##### 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 $\left(p,2\right)$–torus knots with a given colouring when $n=1,2,\dots ,p$. This gives a $3$–colour and a $5$–colour analogue of the surgery presentation of a knot.

##### Keywords
dihedral covering, covering space, Fox colouring, tricoloured knots, surgery presentation
##### Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M10, 57M27
##### Publication
Received: 25 June 2005
Published: 24 May 2006
##### Authors
 Daniel Moskovich Research Institute for Mathematical Sciences Kyoto University Kyoto 606-8502 Japan http://www.sumamathematica.com/