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