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On the Question of Genericity of Hyperbolic Knots. / Малютин, Андрей Валерьевич.

In: International Mathematics Research Notices, Vol. 2020, No. 21, 01.11.2020, p. 7792-7828.

Research output: Contribution to journal › Article › peer-review

Harvard

Малютин, АВ 2020, 'On the Question of Genericity of Hyperbolic Knots', International Mathematics Research Notices, vol. 2020, no. 21, pp. 7792-7828. https://doi.org/10.1093/imrn/rny220

APA

Малютин, А. В. (2020). On the Question of Genericity of Hyperbolic Knots. International Mathematics Research Notices, 2020(21), 7792-7828. https://doi.org/10.1093/imrn/rny220

Vancouver

Малютин АВ. On the Question of Genericity of Hyperbolic Knots. International Mathematics Research Notices. 2020 Nov 1;2020(21):7792-7828. https://doi.org/10.1093/imrn/rny220

Author

Малютин, Андрей Валерьевич. / On the Question of Genericity of Hyperbolic Knots. In: International Mathematics Research Notices. 2020 ; Vol. 2020, No. 21. pp. 7792-7828.

BibTeX

@article{b70a812e42e249dc96c05e5d913c5ee2,
title = "On the Question of Genericity of Hyperbolic Knots",
abstract = "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.",
author = "Малютин, {Андрей Валерьевич}",
note = "Publisher Copyright: {\textcopyright} 2018 The Author(s) 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.",
year = "2020",
month = nov,
day = "1",
doi = "10.1093/imrn/rny220",
language = "English",
volume = "2020",
pages = "7792--7828",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "21",

}

RIS

TY - JOUR

T1 - On the Question of Genericity of Hyperbolic Knots

AU - Малютин, Андрей Валерьевич

N1 - Publisher Copyright: © 2018 The Author(s) 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

PY - 2020/11/1

Y1 - 2020/11/1

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.

UR - https://academic.oup.com/imrn/article/2020/21/7792/5106155?guestAccessKey=a8dc3477-9370-44eb-b444-877db74bbe24

UR - http://www.scopus.com/inward/record.url?scp=85086093099&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/3fba46de-6441-327d-9501-619d623a8f66/

U2 - 10.1093/imrn/rny220

DO - 10.1093/imrn/rny220

M3 - Article

VL - 2020

SP - 7792

EP - 7828

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 21

ER -

ID: 71227095