Geodesic
Knots of (canonical) genus two
A. Stoimenow1
1 BK21 Project Department of Mathematical Sciences KAIST Daejeon, 307-701, Korea
Fundamenta Mathematicae, Tome 200 (2008) no. 1, pp. 1-67 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm200-1-1
Keywords: description knot diagrams canonical genus applications positive alternating homogeneous knots including classification achiral genus alternating knots slice achiral almost positive knots proof move conjectures calculation maximal hyperbolic volume canonical weak genus knots study values link polynomials roots unity extending denseness results jones using these values examples knots non sharp morton canonical genus inequality found several results generalized arbitrary canonical genus

A. Stoimenow 1

1 BK21 Project Department of Mathematical Sciences KAIST Daejeon, 307-701, Korea 
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A. Stoimenow. Knots of (canonical) genus two. Fundamenta Mathematicae, Tome 200 (2008) no. 1, pp. 1-67. doi: 10.4064/fm200-1-1

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