Type: Article
Publication Date: 1973-11-01
Citations: 0
DOI: https://doi.org/10.1017/s1446788700015020
The nullity of the Alexander module of the fundamental group of the complement of a knot in S 3 was one of the invariants of wild knot type defined and investigated by E. J. Brody in [1], in which he developed a generalised elementary divisor theory applicable to infinitely generated modules over a unique factorisation domain. Brody asked whether the nullity of a knot with one wild point was bounded above by its enclosure genus; for knots in S 3 , the present author showed in [6] that this was indeed the case. In [7], it was (prematurely) stated by the author that this was also the case for knots k embedded in a 3-manifold M so that H ,( M — k ) was torsion-free.
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