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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Knot modules and the Nakanishi index
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by C. Kearton and S. M. J. Wilson PDF
Proc. Amer. Math. Soc. 131 (2003), 655-663 Request permission

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.
References
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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
  • 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
  • © Copyright 2002 American Mathematical Society
  • 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
  • MathSciNet review: 1933359