Null-homologous unknottings

  • Charles Livingston

    Indiana University, Bloomington, USA
Null-homologous unknottings cover

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Abstract

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 2gg null-homologous twists and that there exist genus gg knots that cannot be unknotted with fewer than 2gg null-homologous twists.