SIMPLE 4-KNOTS

We show that the isotopy type of a 1-simple n-knot K is determined by the Postnikov (n - 1)-stage of its exterior X(K), together with the ho motopy class of the longitude lambda(K) is an element of pi(n) (X(K)). Moreover any pair (X, j) where X is a 4-dimensional homology circle w ith pi(1) (X) congruent to Z and j : S-4 x S-1 --> X is such that (X, j) = (MCyl(j), S-4 x S-1) is an orientable PD6-pair is realizable by s ome simple 4-knot. We derive complete algebraic characterizations of t orsion free fibred simple 4-knots and of Artin spins of fibred simple 3-knots.