The Vol–Det Conjecture for Highly Twisted Alternating Links | Sciact - Система учета научной деятельности ИМ СО РАН

The Vol–Det Conjecture for Highly Twisted Alternating Links Научная публикация

Журнал

Mathematical Notes
ISSN: 0001-4346 , E-ISSN: 1573-8876

Вых. Данные

Год: 2026, Том: 119, Номер: 1-2, Страницы: 21-28 Страниц : 8 DOI: 10.1134/s0001434626600274

Ключевые слова

knot, link, determinant of link, hyperbolic volume of link complement, twist number.

Авторы

Vesnin A.Yu. ^1,2 , Egorov A.A. ^1,2

Организации

1	Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia
2	Tomsk State University, Tomsk, 634050, Russia

Информация о финансировании (1)

Министерство науки и высшего образования РФ

075-02-2024-1437

The Vol–Det Conjecture by Champanerkar, Kofman and Purcell states that there is an inequality relating the hyperbolic volume of an alternating link and its determinant. The classes of links satisfying this conjecture include all alternating hyperbolic knots with at most 16 crossings, 2-bridge links, and links that are closures of 3-strand braids. We improve Burton’s bound on the number of crossings for which the Vol–Det Conjecture holds for links with more than eight twists. We also strengthen Stoimenow’s inequalities between hyperbolic volumes and determinants for alternating and arborescent (Conway-algebraic) alternating links with more than eight twists.

Vesnin A.Y. , Egorov A.A.
The Vol–Det Conjecture for Highly Twisted Alternating Links
Mathematical Notes. 2026. V.119. N1-2. P.21-28. DOI: 10.1134/s0001434626600274 OpenAlex

Vesnin A.Y. , Egorov A.A.
Гипотеза об объеме и детерминанте для альтернированных зацеплений с большим числом скручиваний
Математические заметки. 2026. Т.119. №1. С.9-18. DOI: 10.4213/mzm14598 OpenAlex

Поступила в редакцию:	8 дек. 2024 г.
Принята к публикации:	22 сент. 2025 г.
Опубликована online:	10 июн. 2026 г.

≡ OpenAlex:

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