The classification of links up to clasp-pass moves

2024/07/22 by Jean–Baptiste Meilhan, Akira Yasuhara, Meilhan, Jean-Baptiste +1
Computer Science · Mathematics · #semigroups and automata theory #Geometric and Algebraic Topology #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.2407.15437

Abstract

We give a complete classification of links up to clasp-pass moves, which coincides with Habiro's C₃-equivalence. We also classify links up to band-pass and band-# moves, which are versions of the usual pass- and #-move, respectively, where each pair of parallel strands belong to the same component. This recovers and generalizes widely a number of partial results in the study of these local moves. The proofs make use of clasper theory.

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