A virtual knot whose virtual unknotting number equals one and a sequence of n-writhes

Yoshiyuki Ohyama, Migiwa Sakurai

研究成果査読

抄録

Satoh and Taniguchi introduced the n-writhe Jn for each non-zero integer n, which is an integer invariant for virtual knots. The sequence of n-writhes {Jn}n0 of a virtual knot K satisfies n0 nJn(K) = 0. They showed that for any sequence of integers {cn}n0 with n0 ncn = 0, there exists a virtual knot K with Jn(K) = cn for any n ≠ 0. It is obvious that the virtualization of a real crossing is an unknotting operation for virtual knots. The unknotting number by the virtualization is called the virtual unknotting number and is denoted by uv. In this paper, we show that if {cn}n≠0 is a sequence of integers with n0 ncn = 0, then there exists a virtual knot K such that uv(K) = 1 and Jn(K) = cn for any n ≠ 0.

本文言語English
ページ(範囲)983
ページ数1
ジャーナルJournal of the Mathematical Society of Japan
73
3
DOI
出版ステータスPublished - 2021

ASJC Scopus subject areas

  • 数学 (全般)

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