2016/12/11 by A. V. Malyutin, Malyutin, Andrei · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #20F36 (Secondary) #20F65 #20F67 #57M25 (Primary) 60G50 #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1612.03368
openalex publication_date 2016/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A well-known conjecture in knot theory says that the percentage of hyperbolic knots amongst all of the prime knots of n or fewer crossings approaches 100 as n approaches infinity. In this paper, 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.