Additivity of bridge numbers of knots
نویسندگان
چکیده
منابع مشابه
Stick Numbers of 2-bridge Knots and Links
Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of the minimal crossing number c(K) of the knot, which is s(K) ≤ 2c(K). Furthermore, McCabe proved that s(K) ≤ c(K) + 3 for a 2-bridge knot or link, except in the cases of the unlink and the Hopf link. In this paper we construct any 2-bridge knot or link K of at least six crossings by using only c(K) + 2 straig...
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It has long been conjectured that the crossing numbers of links are additive under the connected sum of links. This is a difficult problem in knot theory and has been open for more than 100 years. In fact, we do not even know that Cr(K1#K2) = Cr(K1) or Cr(K1#K2) = Cr(K2) holds in general, here K1#K2 is the connected sum of K1 and K2 and Cr(K) stands for the crossing number of the link K. The be...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2003
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004103006832