A Partial Order in the Knot Table

  title={A Partial Order in the Knot Table},
  author={Teruaki Kitano and Masaaki Suzuki},
  journal={Experimental Mathematics},
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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