Geometry & Topology, Vol. 6 (2002) Paper no. 11, pages 355--360.

Burnside obstructions to the Montesinos-Nakanishi 3-move conjecture

Mieczyslaw K Dabkowski Jozef H Przytycki

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.

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

AMS subject classification. Primary: 57M27. Secondary: 20D99.

DOI: 10.2140/gt.2002.6.355

E-print: arXiv:math.GT/0205040

Submitted to GT on 5 May 2002. (Revised 19 June 2002.) Paper accepted 27 June 2002. Paper published 28 June 2002.

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Mieczyslaw K Dabkowski Jozef H Przytycki
Department of Mathematics, The George Washington University
Washington, DC 20052, USA
Email: mdab@gwu.edu, przytyck@gwu.edu

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