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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Burnside obstructions to the Montesinos–Nakanishi $3$–move conjecture

Mieczysław K Dabkowski and Józef H Przytycki

Geometry & Topology 6 (2002) 355–360

arXiv: math.GT/0205040

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 nth 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.

Keywords
knot, link, tangle, 3–move, rational move, braid, Fox coloring, Burnside group, Borromean rings, Montesinos–Nakanishi conjecture, branched cover, core group, lower central series, associated graded Lie ring, skein module
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 20D99
References
Forward citations
Publication
Received: 5 May 2002
Revised: 19 June 2002
Accepted: 26 June 2002
Published: 27 June 2002
Proposed: Robion Kirby
Seconded: Walter Neumann, Vaughan Jones
Authors
Mieczysław K Dabkowski
Department of Mathematics
The George Washington University
Washington
District of Columbia 20052
USA
Józef H Przytycki
Department of Mathematics
The George Washington University
Washington
District of Columbia 20052
USA