TY - JOUR

T1 - On the question of genericity of hyperbolic knots

AU - Malyutin, Andrei V.

PY - 2018

Y1 - 2018

N2 - A well-known conjecture in knot theory says that the proportion of hyperbolic knots among all of the prime knots of n or fewer crossings approaches 1 as n approaches infinity. In this article, it is proved that this conjecture contradicts several other plausible conjectures, including the 120-year-old conjecture on additivity of the crossing number of knots under connected sum and the conjecture that the crossing number of a satellite knot is not less than that of its companion.

AB - A well-known conjecture in knot theory says that the proportion of hyperbolic knots among all of the prime knots of n or fewer crossings approaches 1 as n approaches infinity. In this article, it is proved that this conjecture contradicts several other plausible conjectures, including the 120-year-old conjecture on additivity of the crossing number of knots under connected sum and the conjecture that the crossing number of a satellite knot is not less than that of its companion.

KW - узел

KW - тэнгл

KW - число перекрестков

KW - число развязывания

KW - простой

KW - составной

KW - гиперболический

KW - торический

KW - сателлитный

M3 - Article

VL - 2020

SP - 7792

EP - 7828

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 21

ER -