Open Access
Translator Disclaimer
2009 Surgery presentations of coloured knots and of their covering links
Andrew Kricker, Daniel Moskovich
Algebr. Geom. Topol. 9(3): 1341-1398 (2009). DOI: 10.2140/agt.2009.9.1341


We consider knots equipped with a representation of their knot groups onto a dihedral group D2n (where n is odd). To each such knot there corresponds a closed 3–manifold, the (irregular) dihedral branched covering space, with the branching set over the knot forming a link in it. We report a variety of results relating to the problem of passing from the initial data of a D2n–coloured knot to a surgery presentation of the corresponding branched covering space and covering link. In particular, we describe effective algorithms for constructing such presentations. A by-product of these investigations is a proof of the conjecture that two D2n–coloured knots are related by a sequence of surgeries along ±1–framed unknots in the kernel of the representation if and only if they have the same coloured untying invariant (a n–valued algebraic invariant of D2n–coloured knots).


Download Citation

Andrew Kricker. Daniel Moskovich. "Surgery presentations of coloured knots and of their covering links." Algebr. Geom. Topol. 9 (3) 1341 - 1398, 2009.


Received: 22 August 2008; Revised: 1 June 2009; Accepted: 1 June 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1179.57003
MathSciNet: MR2520403
Digital Object Identifier: 10.2140/agt.2009.9.1341

Primary: 57M12
Secondary: 57M25

Rights: Copyright © 2009 Mathematical Sciences Publishers


Vol.9 • No. 3 • 2009
Back to Top