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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
An Upsilon torsion function for knot Floer homology
Samantha Allen, Charles Livingston
Heegaard Floer theory produces chain complexes associated to knots. Viewed as modules over polynomial rings, such complexes yield torsion invariants that offer constraints on cobor…