TWIST-SPUN KNOTS OF TWIST-SPUN KNOTS OF CLASSICAL KNOTS

A k-twist-spun knot is an (n+1)-dimensional knot in the (n+3)-dimensional sphere that is obtained from an n-dimensional knot in the (n+2)-dimensional sphere by applying an operation called a k-twist-spinning. This construction was introduced by Zeeman (1965). In this paper, we show that the m2-twist-spinning of the m1-twist-spinning of a classical knot is a trivial 3-knot in S5 if gcd(m1, m2) = 1. We also give a sufficient condition for the m2-twist-spinning of the m1-twist-spinning of a classical knot to be nontrivial.