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THE C_k-GORDIAN COMPLEX OF KNOTS

YOSHIYUKI OHYAMA

Department of Mathematics, College 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/S0218216506004300Cited by:14 (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 by using "a crossing change". In this paper, we define the C_k-Gordian complex of knots which is an extension of the Gordian complex of knots. Let k be a natural number more than 2 and we show that for any knot K₀ and any given natural number n, there exists a family of knots {K₀, K₁,…, K_n} such that for any pair (K_i, K_j) of distinct elements of the family, the C_k-distance d_{C_k}(K_i, K_j) = 1.

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AMSC: 57M25

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