Knots of (canonical) genus two

A. Stoimenow. "Knots of (canonical) genus two." Fundamenta Mathematicae 200.1 (2008): 1-67. <http://eudml.org/doc/283152>.

@article{A2008,
abstract = {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.},
author = {A. Stoimenow},
journal = {Fundamenta Mathematicae},
keywords = {knot; knot diagram; Seifert surface; genus; positive knot},
language = {eng},
number = {1},
pages = {1-67},
title = {Knots of (canonical) genus two},
url = {http://eudml.org/doc/283152},
volume = {200},
year = {2008},
}

TY - JOUR
AU - A. Stoimenow
TI - Knots of (canonical) genus two
JO - Fundamenta Mathematicae
PY - 2008
VL - 200
IS - 1
SP - 1
EP - 67
AB - 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.
LA - eng
KW - knot; knot diagram; Seifert surface; genus; positive knot
UR - http://eudml.org/doc/283152
ER -