Self and mixed delta-moves on algebraically split links
Abstract
A delta-move is a local move on a link diagram. The delta-Gordian distance between links measures the minimum number of delta-moves needed to move between link diagrams. A self delta-move only involves a single component of a link whereas a mixed delta-move involves multiple (2 or 3) components. We prove that two links are mixed delta-equivalent precisely when they have the same pairwise linking number and same components; we also give a number of results on how (mixed/self) delta-moves relate to classical link invariants including the Arf invariant and crossing number. This allows us to produce a graph showing links related by a self delta-move for algebraically split links with up to 9-crossings. For these links we also introduce and calculate the delta-splitting number and mixed delta-splitting number, that is, the minimum number of delta-moves needed to separate the components of the link.
Cite
@article{arxiv.2401.07372,
title = {Self and mixed delta-moves on algebraically split links},
author = {Anthony Bosman and Devin Garcia and Justyce Goode and Yamil Kas-Danouche and Davielle Smith},
journal= {arXiv preprint arXiv:2401.07372},
year = {2024}
}
Comments
10 pages, 10 figures, 3 tables