Research ArticleNo Access

Positive knots and weak (1, 3) homotopy

Noboru Ito

http://orcid.org/0000-0001-9011-8982

Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153-8914, Japan

E-mail Address: nito@ibaraki-ct.ac.jp

Corresponding author.

Current address: National Institute of Technology, Ibaraki College, 866 Nakane, Hitachinaka, Ibaraki 312-8508, Japan.

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and

Yusuke Takimura

Gakushuin Boys’ Junior High School, 1-5-1, Mejiro, Toshima-ku, Tokyo 171-0031, Japan

E-mail Address: Yusuke.Takimura@gakushuin.ac.jp

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https://doi.org/10.1142/S0218216520500613Cited by:1 (Source: Crossref)

Abstract

It is known that there exists a surjective map from the set of weak (1, 3) homotopy classes of knot projections to the set of positive knots [N. Ito and Y. Takimura, (1, 2) and weak (1, 3) homotopies on knot projections, J. Knot Theory Ramifications22 (2013) 1350085]. An interesting question whether this map is also injective, which question was formulated independently by S. Kamada and Y. Nakanishi in 2013 (Question q1). This paper obtains an answer to this question.

Keywords:

AMSC: 57K10, 57R42, 57K99

References

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