Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE QUASITORIC BRAID INDEX OF A LINK

  • BAE, YONGJU (DEPARTMENT OF MATHEMATICS KYUNGPOOK NATIONAL UNIVERSITY) ;
  • SEO, SEOGMAN (DEPARTMENT OF MATHEMATICS KYUNGPOOK NATIONAL UNIVERSITY)
  • Received : 2015.01.21
  • Published : 2015.11.01
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Abstract

We dene new link invariants which are called the quasitoric braid index and the cyclic length of a link and show that the quasitoric braid index of link with k components is the product of k and the cycle length of link. Also, we give bounds of Gordian distance between the (p,q)-torus knot and the closure of a braid of two specific quasitoric braids which are called an alternating quasitoric braid and a blockwise alternating quasitoric braid. We give a method of modication which makes a quasitoric presentation from its braid presentation for a knot with braid index 3. By using a quasitoric presentation of $10_{139}$ and $10_{124}$, we can prove that $u(10_{139})=4$ and $d^{\times}(10_{124},K(3,13))=8$.

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Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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