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

2019/03/11 by Carolina Medina, Medina, Carolina, Gelasio Salazar +1
Computer Science · Mathematics · #57M25 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1903.04532

openalex publication_date 2019/03/11 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

Let L be a fixed link. Given a link diagram D, is there a sequence of\ncrossing exchanges and smoothings on D that yields a diagram of L? We\napproach this problem from the computational complexity point of view. It\nfollows from work by Endo, Itoh, and Taniyama that if L is a prime link with\ncrossing number at most 5, then there is an algorithm that answers this\nquestion in polynomial time. We show that the same holds for all torus links\nT2,m and all twist knots.\n

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