TY - JOUR

T1 - On the Question of Genericity of Hyperbolic Knots

AU - Малютин, Андрей Валерьевич

N1 - Andrei V. Malyutin, On the Question of Genericity of Hyperbolic Knots, International Mathematics Research Notices, rny220, https://doi.org/10.1093/imrn/rny220 Published: 24 September 2018

PY - 2018/9/24

Y1 - 2018/9/24

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 - hyperbolicity

KW - knot

KW - satellite

U2 - 10.1093/imrn/rny220

DO - 10.1093/imrn/rny220

M3 - Article

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

ER -