n-valued groups, branched coverings and hyperbolic 3-manifolds | Sciact - Система учета научной деятельности ИМ СО РАН

n-valued groups, branched coverings and hyperbolic 3-manifolds Научная публикация

Журнал

Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802

Вых. Данные

Год: 2024, Том: 215, Номер: 11, Страницы: 1441-1467 Страниц : 27 DOI: 10.4213/sm10089e

Ключевые слова

n-valued group, cyclically presented group, Fibonacci group, branched cyclic covering, three-dimensional manifold, knot.

Авторы

Buchstaber Victor Matveevich ^1,2 , Vesnin Andrei Yurievich ^3,4,5

Организации

1	Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
2	Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
3	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
4	Tomsk State University, Tomsk, Russia
5	Novosibirsk State University, Novosibirsk, Russia

Информация о финансировании (2)

1	Томский государственный университет	НУ 2.0.1.23 ОНТ Приоритет-2030
2	Национальный исследовательский университет "Высшая школа экономики"	Зеркальные лаборатории

The theory of n-valued groups and its applications is developed by going over from groups defined axiomatically to combinatorial groups defined by generators and relations. A wide class of cyclic n-valued groups is introduced on the basis of cyclically presented groups. The best-known cyclically presented groups are the Fibonacci groups introduced by Conway. The problem of the existence of the orbit space of n-valued groups is related to the problem of the integrability of n-valued dynamics. Conditions for the existence of such spaces are presented. Actions of cyclic n-valued groups on R3 with orbit space homeomorphic to S3 are constructed. The projections R3 → S3 onto the orbit space are shown to be connected, by means of commutative diagrams, with coverings of the sphere S3 by three-dimensional compact hyperbolic manifolds which are cyclically branched along a hyperbolic knot. Bibliography: 54 titles

Buchstaber V.M. , Vesnin A.Y.
n-valued groups, branched coverings and hyperbolic 3-manifolds
Sbornik Mathematics. 2024. V.215. N11. P.1441-1467. DOI: 10.4213/sm10089e WOS Scopus OpenAlex

Buchstaber V.M. , Vesnin A.Y.
n-значные группы, разветвленные накрытия и трехмерные гиперболические многообразия
Математический сборник. 2024. Т.215. №11. С.3-32. DOI: 10.4213/sm10089 РИНЦ OpenAlex

Поступила в редакцию:	20 февр. 2024 г.
Опубликована в печати:	21 окт. 2024 г.
Опубликована online:	21 окт. 2024 г.

Web of science:	WOS:001419785700002
Scopus:	2-s2.0-85217959827
OpenAlex:	W4407142779

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