Volume 6, issue 2 (2006)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 (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.

Keywords
dihedral covering, covering space, Fox colouring, tricoloured knots, surgery presentation
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M10, 57M27
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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/