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Knot modules and the Nakanishi index


Authors: C. Kearton and S. M. J. Wilson
Journal: Proc. Amer. Math. Soc. 131 (2003), 655-663
MSC (2000): Primary 57M25; Secondary 57Q45
DOI: https://doi.org/10.1090/S0002-9939-02-06582-6
Published electronically: June 12, 2002
MathSciNet review: 1933359
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Abstract: We examine the structure of the knot module of $9_{38}$ and show that the Nakanishi index of this knot is 2. The Nakanishi indices of $10_{69}$and $10_{101}$ are also determined by means of the Fox-Smythe row class. Finally, we point out that the Nakanishi index is not additive over knot composition.


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Additional Information

C. Kearton
Affiliation: Department of Mathematics, University of Durham, South Road, Durham DH1 3LE, England
Email: Cherry.Kearton@durham.ac.uk

S. M. J. Wilson
Affiliation: Department of Mathematics, University of Durham, South Road, Durham DH1 3LE, England
Email: S.M.J.Wilson@durham.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-02-06582-6
Keywords: Knot module, Nakanishi index, Fox-Smythe, row class
Received by editor(s): May 21, 2001
Received by editor(s) in revised form: October 10, 2001
Published electronically: June 12, 2002
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society

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