Kyungpook Mathematical Journal

  • 제57권1호
  • /
  • Pages.163-185
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  • 2017
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Separating a Chart

  • 투고 : 2016.03.27
  • 심사 : 2016.11.17
  • 발행 : 2017.03.23
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초록

In this paper, we shall show a condition for that a chart is C-move equivalent to the product of two charts, the union of two charts ${\Gamma}^*$ and ${\Gamma}^{**}$ which are contained in disks $D^*$ and $D^{**}$ with $D^*{\cap}D^{**}={\emptyset}$.

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참고문헌

  1. J. S. Carter and M. Saito, Knotted surfaces and their diagrams, Mathematical Surveys and Monographs, 55, American Mathematical Society, Providence, RI, (1998).
  2. J. S. Carter, S. Kamada, and M. Saito, Alexander numbering of knotted surface diagrams,Proc. Amer. Math. Soc., 128(2000), 3761-3771. https://doi.org/10.1090/S0002-9939-00-05479-4
  3. I. Hasegawa, The lower bound of the w-indices of non-ribbon surface-links, Osaka J. Math., 41(2004), 891-909.
  4. S. Ishida, T. Nagase and A. Shima, Minimal n-charts with four white vertices, J. Knot Theory Ramifications, 20(2011), 689-711. https://doi.org/10.1142/S0218216511008899
  5. S. Kamada, Surfaces in $R^4$ of braid index three are ribbon, J. Knot Theory Ramifications, 1(2)(1992), 137-160. https://doi.org/10.1142/S0218216592000082
  6. S. Kamada, An observation of surface braids via chart description, J. Knot Theory Ramifications, 5(4)(1996), 517-529. https://doi.org/10.1142/S0218216596000308
  7. S. Kamada, Braid and Knot Theory in Dimension Four, Mathematical Surveys and Monographs, 95, American Mathematical Society, (2002).
  8. T. Nagase, D. Nemoto and A. Shima, There exists no minimal n-chart of type (2; 2; 2), Proc. Sch. Sci. Tokai Univ., 46(2011), 1-31.
  9. T. Nagase and A. Shima, Properties of minimal charts and their applications I, J. Math. Sci. Univ. Tokyo, 14(2007), 69-97.
  10. T. Nagase and A. Shima, Properties of minimal charts and their applications II, Hiroshima Math. J., 39(2009), 1-35.
  11. T. Nagase and A. Shima, Properties of minimal charts and their applications III, Tokyo J. Math., 33(2010), 373-392. https://doi.org/10.3836/tjm/1296483477
  12. T. Nagase and A. Shima, Properties of minimal charts and their applications IV: Loops, to appear J. Math. Sci. Tokyo J. Math. (arXiv:1603.04639).
  13. T. Nagase and A. Shima, Properties of minimal charts and their applications V-, in preparation.
  14. T. Nagase and A. Shima, Gambits in charts, J. Knot Theory Ramifications, 24(9) (2015), 1550052 (21 pages). https://doi.org/10.1142/S0218216515500522
  15. T. Nagase, A. Shima and H. Tsuji, The closures of surface braids obtained from minimal n-charts with four white vertices, J. Knot Theory Ramifications, 22(2)(2013) 1350007 (27 pages). https://doi.org/10.1142/S0218216513500077
  16. M. Ochiai, T. Nagase and A. Shima, There exists no minimal n-chart with five white vertices, Proc. Sch. Sci. Tokai Univ., 40(2005), 1-18.
  17. K. Tanaka, A Note on CI-moves, Intelligence of Low Dimensional Topology 2006 Eds. J. Scott Carter et al. (2006), 307-314.