Surgery untying of coloured knots

Moskovich, Daniel

doi:10.2140/agt.2006.6.673

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Surgery untying of coloured knots

Daniel Moskovich

Algebraic & Geometric Topology 6 (2006) 673–697

DOI: 10.2140/agt.2006.6.673

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 $\pm 1$ –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 $n = 1, 2, \dots, p$ . 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

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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/

Volume 6, issue 2 (2006)