# Simple 4-knots

## Author

**J. A. Hillman** and **C. Kearton**

## Status

Research Report 97-26

Date: 26 September 1997

## Abstract

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.

## Key phrases

fibred knot. 4-knot. Poincare duality. Postnikov. simple knot.

## AMS Subject Classification (1991)

Primary: 57Q45

Secondary:

## Content

The paper is available in the following forms:
- TeX dvi format:
- 1997-26.dvi.gz (23kB) or
1997-26.dvi (57kB)

- PostScript:
- 1997-26.ps.gz (50kB) or
1997-26.ps (155kB)

##### To minimize network load, please choose the smaller gzipped .gz form if
and only if your browser client supports it.

Sydney Mathematics and Statistics