Algebraic & Geometric Topology

Surgery untying of coloured knots

Daniel Moskovich

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796541

Digital Object Identifier
doi:10.2140/agt.2006.6.673

Mathematical Reviews number (MathSciNet)
MR2240912

Zentralblatt MATH identifier
1098.57007

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

Keywords
dihedral covering covering space Fox colouring tricoloured knots surgery presentation

Citation

Moskovich, Daniel. Surgery untying of coloured knots. Algebr. Geom. Topol. 6 (2006), no. 2, 673--697. doi:10.2140/agt.2006.6.673. https://projecteuclid.org/euclid.agt/1513796541


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