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Determinants of knots and Diophantine equations

100%

Stoimenow A.

Acta Arithmetica

2007

tom 129

nr 4

363-387

Knots of (canonical) genus two

100%

Stoimenow A.

Fundamenta Mathematicae

2008

tom 200

nr 1

1-67

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.

Ograniczanie wyników

1 Acta Arithmetica

1 Fundamenta Mathematicae

2 Stoimenow A.

1 2008

1 2007

Wyniki wyszukiwania

Determinants of knots and Diophantine equations

Knots of (canonical) genus two