THE GORDIAN COMPLEX OF VIRTUAL KNOTS

DOI Web Site 被引用文献2件 参考文献3件
  • SUMIKO HORIUCHI
    Department of Mathematics, School of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1, Zempukuji, Suginami-ku, Tokyo 167-8585, Japan
  • KASUMI KOMURA
    Department of Mathematics, School of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1, Zempukuji, Suginami-ku, Tokyo 167-8585, Japan
  • YOSHIYUKI OHYAMA
    Department of Mathematics, School of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1, Zempukuji, Suginami-ku, Tokyo 167-8585, Japan
  • MASAFUMI SHIMOZAWA
    Department of Mathematics, School of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1, Zempukuji, Suginami-ku, Tokyo 167-8585, Japan

書誌事項

公開日
2012-12
資源種別
journal article
DOI
  • 10.1142/s0218216512501222
公開者
World Scientific Pub Co Pte Lt

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説明

<jats:p> Hirasawa and Uchida defined the Gordian complex of knots which is a simplicial complex whose vertices consist of all knot types in S<jats:sup>3</jats:sup>. In this paper, we define the Gordian complex of virtual knots which is a simplicial complex whose vertices consist of all virtual knots by using the local move which makes a real crossing a virtual crossing. We show that for any virtual knot K<jats:sub>0</jats:sub> and for any given natural number n, there exists a family of virtual knots {K<jats:sub>0</jats:sub>, K<jats:sub>1</jats:sub>,…,K<jats:sub>n</jats:sub>} such that for any pair (K<jats:sub>i</jats:sub>, K<jats:sub>j</jats:sub>) of distinct elements of the family, the Gordian distance of virtual knots d<jats:sub>v</jats:sub>(K<jats:sub>i</jats:sub>, K<jats:sub>j</jats:sub>) = 1. And we also give a formula of the f-polynomial for the sum of tangles of virtual knots. </jats:p>

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