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THE GORDIAN COMPLEX OF VIRTUAL KNOTS BY FORBIDDEN MOVES

Division of Mathematical Sciences, School of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1 Zempukuji, Suginami-ku, Tokyo 167-8585, Japan

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YOSHIYUKI OHYAMA

Division of Mathematical Sciences, School of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1 Zempukuji, Suginami-ku, Tokyo 167-8585, Japan

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https://doi.org/10.1142/S021821651350051XCited by:2 (Source: Crossref)

Abstract

Hirasawa and Uchida defined the Gordian complex of knots which is a simplicial complex whose vertices consist of all knot types in S³. In this paper, we define the Gordian complex of virtual knots by using forbidden moves. We show that for any virtual knot K₀ and for any given natural number n, there exists a family of virtual knots {K₀, K₁, …, K_n} such that for any pair (K_i, K_j) of distinct elements of the family, the Gordian distance of virtual knots by forbidden moves d_F(K_i, K_j) = 1.