J. A. Hillman and C. Kearton
Research Report 97-26
Date: 26 September 1997
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
homotopy class of the longitude $\lambda_K$ in $\pi_n(X(K))$.
Moreover any pair $(X,j)$ where $X$ is a 4-dimensional homology circle with
$\pi_1(X)\cong Z$ and $j:S^4\times S^1\to X$ is a map such that
$(X,j)=(MCyl(j),S^4\times S^1)$ is an orientable $PD_6$-pair is realizable by
some simple 4-knot.
As a consequence we are able to characterize completely the
Artin spins of fibred simple 3-knots.
fibred knot. 4-knot. Poincare duality. Postnikov. simple knot.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics