A Partial Order in the Knot Table

@article{Kitano2005APO,
  title={A Partial Order in the Knot Table},
  author={Teruaki Kitano and Masaaki Suzuki},
  journal={Experimental Mathematics},
  year={2005},
  volume={14},
  pages={385-390}
}
Let K be a prime knot and G(K) its knot group. It is well known that a partial order can be defined on the set of prime knots as follows: for two knots K1,K2, we write K1 ≥ K2 if there exists a surjective group homomorphism from G(K1) onto G(K2). In this paper, we determine this partial order “≥” on the set of knots in Rolfsen’s knot table, which lists all the prime knots of ten crossings or less. Theorem 1.1 is the main result of this paper. The numbering of the knots follows that of Rolfsen’s… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 10 references

and M

  • T. Kitano, M. Suzuki
  • Wada. “Twisted Alexander Polynomial and…
  • 2005
2 Excerpts

KNOT.” Available from World Wide Web (http://www.math.kobe-u.ac.jp/HOME/ kodama/knot.html)

  • K. Kodama
  • 2004
2 Excerpts

Knots and Links

  • D. Rolfsen
  • Providence, RI: AMS Chelsea Publishing
  • 2003
2 Excerpts

Twisted Alexander Polynomial and Reidemeister Torsion.

  • T. Kitano
  • Pacific J. Math
  • 1996
2 Excerpts

Twisted Alexander Polynomial for Finitely Presentable Groups.

  • M. Wada
  • Topology
  • 1994
3 Excerpts

Rei - demeister Torsion , Twisted Alexander Polynomial and Fibered Knots . ” Comment

  • T. Kitano, T. Morifuji
  • Introduction to Knot Theory , Graduate Texts in…
  • 1977

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