The classification of links up to clasp-pass moves
Jean–Baptiste Meilhan, Akira Yasuhara · Canadian Journal of Mathematics · 2025
Abstract We give a complete classification of links up to clasp-pass moves, which coincides with Habiro’s $C_3$ -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.