# Null-homologous unknottings

• ### Charles Livingston

Indiana University, Bloomington, USA

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