Nullification number and flyping conjecture (Q1192067)

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 \textit{W. W. Menasco} and \textit{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.