Affiliation:
1. Department of Mathematics, School of Arts and Sciences, Tokyo Woman's Christian University, 2-6-1, Zempukuji, Suginami-ku, Tokyo 167-8585, Japan
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 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 K0 and for any given natural number n, there exists a family of virtual knots {K0, K1,…,Kn} such that for any pair (Ki, Kj) of distinct elements of the family, the Gordian distance of virtual knots dv(Ki, Kj) = 1. And we also give a formula of the f-polynomial for the sum of tangles of virtual knots.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
6 articles.
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1. The Gordian complex of theta-curves;Journal of Knot Theory and Its Ramifications;2021-07
2. Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves;Journal of Knot Theory and Its Ramifications;2020-08-21
3. A note on the Gordian complexes of some local moves on knots;Journal of Knot Theory and Its Ramifications;2018-08
4. The H(n)-Gordian complex of knots;Journal of Knot Theory and Its Ramifications;2017-11
5. Virtual unknotting numbers of certain virtual torus knots;Journal of Knot Theory and Its Ramifications;2017-10