The delta-unlinking number of algebraically split links
Abstract
It is known that algebraically split links (links with vanishing pairwise linking number) can be transformed into the trivial link by a series of local moves on the link diagram called delta-moves; we define the delta-unlinking number to be the minimum number of such moves needed. This generalizes the notion of delta-unknotting number, defined to be the minimum number of delta-moves needed to move a knot into the unknot. While the delta-unknotting number has been well-studied and calculated for prime knots, no prior such analysis has been conducted for the delta-unlinking number. We prove a number of lower and upper bounds on the delta-unlinking number, relating it to classical link invariants including unlinking number, 4-genus, and Arf invariant. This allows us to determine the precise value of the delta-unlinking number for algebraically split prime links with up to 9 crossings as well as determine the 4-genus for most of these links.
Keywords
Cite
@article{arxiv.2107.06791,
title = {The delta-unlinking number of algebraically split links},
author = {Anthony Bosman and Jeannelle Green and Gabriel Palacios and Moises Reyes and Noe Reyes},
journal= {arXiv preprint arXiv:2107.06791},
year = {2021}
}
Comments
12 pages, 15 figures