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Crosscap number and knot projections

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: noboru@ms.u-tokyo.ac.jp

Corresponding author.

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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/S0129167X18500842Cited by:7 (Source: Crossref)

Abstract

We introduce an unknotting-type number of knot projections that gives an upper bound of the crosscap number of knots. We determine the set of knot projections with the unknotting-type number at most two, and this result implies classical and new results that determine the set of alternating knots with the crosscap number at most two.

Keywords:

AMSC: 57M25

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