Self and Mixed Delta-Moves on Algebraically Split Links
DOI:
https://doi.org/10.46787/pump.v8i.4023Keywords:
delta-move; delta-Gordian distance; linking number; algebraically split linksAbstract
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; 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.
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Copyright (c) 2025 Anthony Bosman, Devin Garcia, Justyce Goode, Yamil Kas-Danouche, Davielle Smith

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.