Self and Mixed Delta-Moves on Algebraically Split Links

Authors

  • Anthony Bosman Andrews University
  • Devin Garcia Andrews University
  • Justyce Goode Andrews University
  • Yamil Kas-Danouche Andrews University
  • Davielle Smith Andrews University

DOI:

https://doi.org/10.46787/pump.v8i.4023

Keywords:

delta-move; delta-Gordian distance; linking number; 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; 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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Published

2025-06-27

How to Cite

Bosman, A., Garcia, D., Goode, J., Kas-Danouche, Y., & Smith, D. (2025). Self and Mixed Delta-Moves on Algebraically Split Links. The PUMP Journal of Undergraduate Research, 8, 273–285. https://doi.org/10.46787/pump.v8i.4023