Burnside obstructions to the Montesinos-Nakanishi 3-move conjecture

Abstract

Yasutaka Nakanishi asked in 1981 whether a 3-move is an unknotting operation. In Kirby's problem list, this question is called `The Montesinos-Nakanishi 3-move conjecture'. We define the n-th Burnside group of a link and use the 3rd Burnside group to answer Nakanishi's question; ie, we show that some links cannot be reduced to trivial links by 3-moves.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper11.abs.html

Cited by in corpus (9)

• Problems on invariants of knots and 3-manifolds
• On core quandles of groups
• Classification of string links up to $2n$-moves and link-homotopy
• Burnside groups and $n$-moves for links
• 3-coloring and other elementary invariants of knots
• Invariants for trivalent tangles and handlebody-tangles
• Generalized virtualization on welded links
• Milnor invariants, $2n$-moves and $V^n$-moves for welded string links
• Ineffectiveness of homotopical invariants on Nakanishi's 4-move conjecture