Construction by isotopy. II

Abstract

Construction by isotopy is a technique introduced by Iain R. Aitchison for obtaining doubly slice fibered knots in any dimension. We show that if k k is any doubly slice fibered ( n − 2 ) (n - 2) -knot, n ⩾ 5 n \geqslant 5 , such that π 1 ( S n − k ) ≅ Z {\pi _1}({S^n} - k) \cong Z , then k k is constructible by isotopy. We also prove that the m m -twist-spin of any doubly slice knot is constructible by isotopy. Consequently, there exists a double slice knot constructible by isotopy that is not the double of any disk knot. We also give an example of a doubly slice fibered 6 6 -knot that is not constructible by isotopy.