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math.GT2022
Unknotting via null-homologous twists and multi-twists
Samantha Allen, Kenan Ince, Seungwon Kim +2
The untwisting number of a knot K is the minimum number of null-homologous twists required to convert K to the unknot. Such a twist can be viewed as a generalization of a crossing…
math.GT2022
Seifert surfaces in the 4-ball
Kyle Hayden, Seungwon Kim, Maggie Miller +2
We answer a question of Livingston from 1982 by producing Seifert surfaces of the same genus for a knot in that do not become isotopic when their interiors are pushed into $B…