Algebraic & Geometric Topology

Surgery untying of coloured knots

Daniel Moskovich

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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.

Article information

Algebr. Geom. Topol., Volume 6, Number 2 (2006), 673-697.

Received: 25 June 2005
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M10: Covering spaces 57M27: Invariants of knots and 3-manifolds

dihedral covering covering space Fox colouring tricoloured knots surgery presentation


Moskovich, Daniel. Surgery untying of coloured knots. Algebr. Geom. Topol. 6 (2006), no. 2, 673--697. doi:10.2140/agt.2006.6.673.

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