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Zbl 0754.57003
Sola, Dino
Nullification number and flyping conjecture. (English)
[J] Rend. Semin. Mat. Univ. Padova 86, 1-16 (1991). ISSN 0041-8994

In analogy to the unknotting number of a knot or link, in the present paper a nullification number is introduced and discussed. For a planar projection of a link, this is the minimal number of ``nullifications'' of crossings which are needed to arrive at a trivial link. For minimal alternating projections this number is easy to compute and depends only on the link. The alternating links with nullification number 1, 2 and $n- 1$ are classified where $n$ denotes the number of crossings of the link. It follows that these links have a unique alternating projection, thus confirming the ``Tait flyping conjecture'' for these links. Note that recently a complete solution of this conjecture has been announced by {\it W. W. Menasco} and {\it M. B. Thistlethwaite} [Bull. Am. Math. Soc. 25, No. 2, 403-412 (1991; Zbl 0745.57002)] stating that alternating projections of links are basically unique.
[B.Zimmermann (Trieste)]

MSC 2000:: *57M25 Knots and links in the 3-sphere

Keywords: minimal projection; Tait flyping conjecture; nullification number; alternating links

Citations: Zbl 0745.57002

Cited in: Zbl 0893.57008

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