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The nullity of a wild knot in a compact 3-manifold

Published online by Cambridge University Press:  09 April 2009

James M. McPherson
James M. McPherson
Affiliation:
School of General Studies Australian National UniversityCanberra.
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The nullity of the Alexander module of the fundamental group of the complement of a knot in S3 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 S3, 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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 3 , November 1973 , pp. 262 - 271
Copyright
Copyright © Australian Mathematical Society 1973

References

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