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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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

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

First available in Project Euclid: 1 August 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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. https://projecteuclid.org/euclid.mjms/1312232716

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  • C. Adams, The Knot Book, American Mathematical Society, Providence, RI, 2000.
  • P. Hackney, L. Van Wyk, N. Walters, $k$-Alternating knots, Topology and its Applications, 150 (2005), 125–131.
  • C. Livingston, Knot Theory, The Mathematical Association of America, Washington, DC, 1993.
  • K. Murasugi, On periodic knots, Commentarii Mathematici Helvetici, 46 (1971), 162–174.
  • K. Murasugi, On the braid index of alternating links, Trans. Amer. Math. Soc. 326 (1991), 237–260.
  • D. Rolfsen, Knots and Links, Publish or Perish, Houston, 1990.