Geodesic
Burnside obstructions to the Montesinos–Nakanishi 3–move conjecture
Dabkowski, Mieczysław K1 ; Przytycki, Józef H1
1 Department of Mathematics, The George Washington University, Washington, District of Columbia 20052, USA
Geometry & topology, Tome 6 (2002) no. 1, pp. 355-360.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.2002.6.355
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

Dabkowski, Mieczysław K 1 ; Przytycki, Józef H 1

1 Department of Mathematics, The George Washington University, Washington, District of Columbia 20052, USA 
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Dabkowski, Mieczysław K; Przytycki, Józef H. Burnside obstructions to the Montesinos–Nakanishi 3–move conjecture. Geometry & topology, Tome 6 (2002) no. 1, pp. 355-360. doi : 10.2140/gt.2002.6.355. http://geodesic.mathdoc.fr/articles/10.2140/gt.2002.6.355/

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