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arXiv · 2210.11067

A note on knot fertility II

Tetsuya Ito
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Abstract

A knot $K$ is called $(m,n)$-fertile if for every prime knot $K'$ whose crossing number is less than or equal to $m$, there exists an $n$-crossing diagram of $K$ such that one can get $K'$ from the diagram by changing its over-under information. We give an obstruction for knot to be $(m,n)$-fertile. As application, we prove the finiteness of $(c(K)+f,c(K)+p)$-fertile knots for all $f,p$. We also discuss the nubmer of Seiefrt circle and writhe of minimum crossing diagrams.

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Tetsuya Ito. 2022-10-20. A note on knot fertility II. https://doi.org/10.1007/s10474-023-01317-7

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