Crosscap number and knot projections-Reference-Cited by-同舟云学术

Crosscap number and knot projections

Published:2018-11 Issue:12 Volume:29 Page:1850084
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Ito Noboru¹^ORCID,Takimura Yusuke²

Affiliation:

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

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

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.

Funder

Sumitomo Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X18500842

Reference15 articles.

1. A classification of spanning surfaces for alternating links

2. Computing the Crosscap Number of a Knot Using Integer Programming and Normal Surfaces

3. Knot Enumeration Through Flypes and Twisted Splices

4. Crosscaps and knotes

5. Incompressible surfaces in 2-bridge knot complements

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