Unknotting submanifolds of the 3-sphere by twistings

• Makoto Ozawa ^[1]
  1. [1] Komazawa University

     Komazawa University

     Japón

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 18, Nº 3, 2018, págs. 1145-1153
• Idioma: inglés
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• Resumen

  • By the Fox’s re-embedding theorem, any compact submanifold of the 3-sphere can be re-embedded in the 3-sphere so that it is unknotted. It is unknown whether the Fox’s re-embedding can be replaced with twistings. In this paper, we will show that any closed 2-manifold embedded in the 3-sphere can be unknotted by twistings. In spite of this phenomenon, we show that there exists a compact 3- submanifold of the 3-sphere which cannot be unknotted by twistings. This shows that the Fox’s re-embedding cannot always be replaced with twistings.