The classification of links up to clasp-pass moves

Jean-Baptiste Meilhan; Akira Yasuhara

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arXiv · 2407.15437

The classification of links up to clasp-pass moves

Jean-Baptiste Meilhan·Akira Yasuhara

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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.

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Jean-Baptiste Meilhan, Akira Yasuhara. 2024-07-22. The classification of links up to clasp-pass moves. https://arxiv.org/abs/2407.15437

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