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Burnside obstructions to
the Montesinos–Nakanishi $3$–move conjecture
Mieczysław K Dabkowski and Józef H Przytycki |
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Geometry & Topology 6 (2002) 355–360
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arXiv: math.GT/0205040 |
Abstract |
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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 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. |
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
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Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 20D99
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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
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Authors |
| Mieczysław K Dabkowski | |
| Department of Mathematics The George Washington University Washington District of Columbia 20052 USA |
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| Józef H Przytycki | |
| Department of Mathematics The George Washington University Washington District of Columbia 20052 USA |
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