Knots of (canonical) genus two

• Autorzy: A. Stoimenow
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds
• 57M25: Knots and links in S 3
• 22E10: General properties and structure of complex Lie groups
• 57M50: Geometric structures on low-dimensional manifolds
• 20F36: Braid groups; Artin groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 200
• Numer: 1
• Strony: 1-67

Daty

wydano

2008

Twórcy

autor

A. Stoimenow

• BK21 Project, Department of Mathematical Sciences, KAIST, Daejeon, 307-701, Korea

Identyfikatory

DOI

10.4064/fm200-1-1