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

n-valued groups, branched coverings and hyperbolic 3-manifolds Full article

Journal

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

Output data

Year: 2024, Volume: 215, Number: 11, Pages: 1441-1467 Pages count : 27 DOI: 10.4213/sm10089e

Tags

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

Authors

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

Affiliations

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

Funding (2)

1	Tomsk State University	НУ 2.0.1.23 ОНТ Приоритет-2030
2	National Research University Higher School of Economics	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 РИНЦ 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

Submitted:	Feb 20, 2024
Published print:	Oct 21, 2024
Published online:	Oct 21, 2024

Web of science:	WOS:001419785700002
Scopus:	2-s2.0-85217959827
Elibrary:	81971369
OpenAlex:	W4407142779

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