TWIST MOVES AND VASSILIEV INVARIANTS.

The transforms of two oriented parallel strands to a k-half twist of two strands are called tk-move and &tmacr;k-move respectively depending on the orientations of the two strands. In this paper we give criterions to detect whether a knot K can be transformed to a knot K' by t2k-moves and t2k-moves respectively and if so, we give some results on how many moves are needed in these transformations respectively, by using some Vassiliev invariants. Moreover we give a relation between the Δ-move and the t2k-move by considering the coefficient of z2 in the Conway polynomial of a knot, which is a Vassiliev invariant of degree 2. [ABSTRACT FROM AUTHOR]