When can a link be obtained from another using crossing exchanges and smoothings?

Carolina Medina; Gelasio Salazar

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arXiv · 1903.04532

When can a link be obtained from another using crossing exchanges and smoothings?

Carolina Medina·Gelasio Salazar

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Abstract

Let $L$ be a fixed link. Given a link diagram $D$, is there a sequence of crossing exchanges and smoothings on $D$ that yields a diagram of $L$? We approach this problem from the computational complexity point of view. It follows from work by Endo, Itoh, and Taniyama that if $L$ is a prime link with crossing number at most $5$, then there is an algorithm that answers this question in polynomial time. We show that the same holds for all torus links $T_{2,m}$ and all twist knots.

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Carolina Medina, Gelasio Salazar. 2019-03-11. When can a link be obtained from another using crossing exchanges and smoothings?. https://arxiv.org/abs/1903.04532

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