Volume 6, issue 2 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23, 1 issue

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
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
References
Forward citations
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/