The classification of links up to clasp-pass moves
Geometric Topology
2025-07-08 v2
Abstract
We give a complete classification of links up to clasp-pass moves, which coincides with Habiro's -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.
Cite
@article{arxiv.2407.15437,
title = {The classification of links up to clasp-pass moves},
author = {Jean-Baptiste Meilhan and Akira Yasuhara},
journal= {arXiv preprint arXiv:2407.15437},
year = {2025}
}
Comments
30 pages. Final version, to appear in Canadian J. Math