## Algebraic & Geometric Topology

### Surgery untying of coloured knots

Daniel Moskovich

#### 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
First available in Project Euclid: 20 December 2017

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

#### 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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