Unknotting genus one knots

• Autores: Alexander Coward, Marc Lackenby
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 86, Nº 2, 2011, págs. 383-399
• Idioma: inglés
• DOI: 10.4171/cmh/227
• Texto completo no disponible (Saber más ...)
• Resumen

  • For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove that there is exactly one way to unknot it by means of a crossing change. In the case of the figure-eight knot, we prove that there are precisely two unknotting crossing changes. The proof uses sutured manifold theory and an analysis of the arc complex of the once-punctured torus.