Knots of (canonical) genus two

• Autores: Alexander Stoimenow
• Localización: Fundamenta mathematicae, ISSN 0016-2736, Vol. 200, Nº 1, 2008, págs. 1-67
• Idioma: inglés
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• Resumen

  • We give a description of all knot diagrams of canonical genus 2 and 3, and give applications to positive, alternating and homogeneous knots, including a classification of achiral genus 2 alternating knots, slice or achiral 2-almost positive knots, a proof of the 3- and 4-move conjectures, and the calculation of the maximal hyperbolic volume for canonical (weak) genus 2 knots. We also study the values of the link polynomials at roots of unity, extending denseness results of Jones. Using these values, examples of knots with non-sharp Morton (canonical genus) inequality are found. Several results are generalized to arbitrary canonical genus.