English

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 C3C_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.

Keywords

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