P-21 The delta-unlinking number of algebraically split links

Presenter Status

Student

Second Presenter Status

Student

Third Presenter Status

Student

Fourth Presenter Status

Student

Fifth Presenter Status

Assistant Professor of Mathematics

Preferred Session

Poster Session

Location

Buller Hall Hallways

Start Date

22-10-2021 2:00 PM

End Date

22-10-2021 3:00 PM

Presentation 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 deltaunlinking number for algebraically split prime links with up to 9 crossings as well as determine the 4-genus for most of these links.

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Oct 22nd, 2:00 PM Oct 22nd, 3:00 PM

P-21 The delta-unlinking number of algebraically split links

Buller Hall Hallways

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 deltaunlinking number for algebraically split prime links with up to 9 crossings as well as determine the 4-genus for most of these links.