A note on knot fertility

Abstract

We show that a knot whose minimum crossing number $c(K)$ is even and greater than $30$ is not fertile; there exists a knot $K^{\prime }$ with crossing number less than $c$ such that $K^{\prime }$ is not obtained from a minimum crossing number diagram of $K$ by suitably changing the over-under information.

3 pages, no figures

Cited by in corpus (2)

• A quantitative Birman-Menasco finiteness theorem and its application to crossing number
• A note on knot fertility II