Missouri Journal of Mathematical Sciences

Spiral Knots

N. Brothers, S. Evans, L. Taalman, L. Van Wyk, D. Witczak, and C. Yarnall

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Abstract

Spiral knots are a generalization of torus knots we define by a certain periodic closed braid representation. For spiral knots with prime power period, we calculate their genus, bound their crossing number, and bound their $m$-alternating excess.

Article information

Source
Missouri J. Math. Sci., Volume 22, Issue 1 (2010), 10-18.

Dates
First available in Project Euclid: 1 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1312232716

Digital Object Identifier
doi:10.35834/mjms/1312232716

Mathematical Reviews number (MathSciNet)
MR2650057

Zentralblatt MATH identifier
1197.57004

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

Citation

Brothers, N.; Evans, S.; Taalman, L.; Van Wyk, L.; Witczak, D.; Yarnall, C. Spiral Knots. Missouri J. Math. Sci. 22 (2010), no. 1, 10--18. doi:10.35834/mjms/1312232716. https://projecteuclid.org/euclid.mjms/1312232716


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References

  • C. Adams, The Knot Book, American Mathematical Society, Providence, RI, 2000.
    Mathematical Reviews (MathSciNet): MR2079925
  • P. Hackney, L. Van Wyk, N. Walters, $k$-Alternating knots, Topology and its Applications, 150 (2005), 125–131.
    Mathematical Reviews (MathSciNet): MR2133673
    Zentralblatt MATH: 1067.57004
    Digital Object Identifier: doi:10.1016/j.topol.2004.11.007
  • C. Livingston, Knot Theory, The Mathematical Association of America, Washington, DC, 1993.
    Mathematical Reviews (MathSciNet): MR1253070
  • K. Murasugi, On periodic knots, Commentarii Mathematici Helvetici, 46 (1971), 162–174.
    Mathematical Reviews (MathSciNet): MR292060
    Zentralblatt MATH: 0206.25603
    Digital Object Identifier: doi:10.1007/BF02566836
  • K. Murasugi, On the braid index of alternating links, Trans. Amer. Math. Soc. 326 (1991), 237–260.
    Mathematical Reviews (MathSciNet): MR1000333
    Zentralblatt MATH: 0751.57008
    Digital Object Identifier: doi:10.2307/2001863
  • D. Rolfsen, Knots and Links, Publish or Perish, Houston, 1990.
    Mathematical Reviews (MathSciNet): MR1277811

University of Central Missouri, Department of Mathematics and Computer Science

Missouri Journal of Mathematical Sciences

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