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A Partial Order in the Knot Table Ⅱ

A Partial Order in the Knot Table Ⅱ
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摘要 A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups. In the previous paper, we determined the partial order in the knot table. In this paper, we prove that 31 and 41 are minimal elements. Further, we study which surjection a pair of a periodic knot and its quotient knot induces, and which surjection a degree one map can induce. A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups. In the previous paper, we determined the partial order in the knot table. In this paper, we prove that 31 and 41 are minimal elements. Further, we study which surjection a pair of a periodic knot and its quotient knot induces, and which surjection a degree one map can induce.
作者 Teruaki KITANO Masaaki SUZUKI
机构地区 Department of Information Systems Science Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第11期1801-1816,共16页 数学学报（英文版）
基金 Grand-in-Aid for Scientific Research (No.17540064 and No.18840008)
关键词 KNOT partial order surjective homomorphism PERIOD degree one map knot, partial order, surjective homomorphism, period, degree one map
分类号 O153.1 [理学—基础数学]
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参考文献16

  • 1Whitten, W.: Knot complements and groups. Topology, 26, 41-44 (1987)
  • 2Gordon, C., Luecke, J.: Knots are determined by their complements. J. Amer. Math. Soc., 2(2), 371-415 (1989)
  • 3Kawauchi, A. (ed): A Survey of Knot Theory, Birkhaiiser Verlag, Basel, 1996
  • 4Kitano, T., Suzuki, M.: A partial order on the knot table. Experimental Math., 14, 385-390 (2005)
  • 5Rolfsen, D.: Knots and links, AMS Chelsea Publishing
  • 6Neuwirth, L.: Knot Groups, Annals of Mathematics Studies, No. 56 Princeton University Press, Princeton, N.J., 1965
  • 7Stallings, J.: On fibering certain 3-manifolds, 1962 Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) 95-100 Prentice Hall, Englewood Cliffs, N.J.
  • 8Silver, D., Whitten, W.: Knot group epimorphisms. J. Knot Theory Ramifications, 15, 153-166 (2006)
  • 9Hempel, J.: 3-manifolds, Reprint of the 1976 original. AMS Chelsea Publishing, Providence, RI, 2004
  • 10Papakyriakopoulos, C. D.: On Dehn's lemma and the asphericity of knots. Ann. of Math. (2), 66, 1-26 (1957)
Acta Mathematica Sinica,English Series
2008年 第11期

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