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Null-homologous unknottings

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arxiv 1902.05405 v2 pith:CU5KOLTH submitted 2019-02-14 math.GT

Charles Livingston This is my paper · ORCID
classification math.GT
keywords null-homologoustwistsunknottedgenusknotcannoteveryexist
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Every knot can be unknotted with two generalized twists; this was first proved by Ohyama. Here we prove that any knot of genus g can be unknotted with 2g null-homologous twists and that there exist genus g knots that cannot be unknotted with fewer than 2g null-homologous twists.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Untwisting 3-strand torus knots

    math.GT 2019-09 conditional novelty 7.0 of 10

    The topological 4-genus of every 3-strand torus knot equals half its maximal signature and its untwisting number.

  2. Null-homologous twisting and the algebraic genus

    math.GT 2019-08 conditional novelty 6.0 of 10

    Null-homologous twists change the algebraic genus by at most one under a square condition, yielding new upper bounds on the topological slice genus of torus knots and satellite knots.

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