Volume 6, issue 2 (2006)

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

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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/