Self and mixed delta-moves on algebraically split links

Anthony Bosman; Devin Garcia; Justyce Goode; Yamil Kas-Danouche; Davielle Smith

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arXiv · 2401.07372

Self and mixed delta-moves on algebraically split links

Anthony Bosman·Devin Garcia·Justyce Goode·Yamil Kas-Danouche·Davielle Smith

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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.

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BibTeX RIS

Anthony Bosman, Devin Garcia, Justyce Goode, Yamil Kas-Danouche, Davielle Smith. 2024-01-14. Self and mixed delta-moves on algebraically split links. https://arxiv.org/abs/2401.07372

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