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n-valued groups, branched coverings and hyperbolic 3-manifolds. / Buchstaber, Victor M.; Vesnin, Andrei Yu.

In: Sbornik Mathematics, Vol. 215, No. 11, 2024, p. 1441-1467.

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

Harvard

Buchstaber, VM & Vesnin, AY 2024, 'n-valued groups, branched coverings and hyperbolic 3-manifolds', Sbornik Mathematics, vol. 215, no. 11, pp. 1441-1467. https://doi.org/10.4213/sm10089e

APA

Buchstaber, V. M., & Vesnin, A. Y. (2024). n-valued groups, branched coverings and hyperbolic 3-manifolds. Sbornik Mathematics, 215(11), 1441-1467. https://doi.org/10.4213/sm10089e

Vancouver

Buchstaber VM, Vesnin AY. n-valued groups, branched coverings and hyperbolic 3-manifolds. Sbornik Mathematics. 2024;215(11):1441-1467. doi: 10.4213/sm10089e

Author

Buchstaber, Victor M. ; Vesnin, Andrei Yu. / n-valued groups, branched coverings and hyperbolic 3-manifolds. In: Sbornik Mathematics. 2024 ; Vol. 215, No. 11. pp. 1441-1467.

BibTeX

@article{f3d5a4d68f23434f966f41cc43bc2b27,
title = "n-valued groups, branched coverings and hyperbolic 3-manifolds",
abstract = "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.",
keywords = "Fibonacci group, branched cyclic covering, cyclically presented group, knot, n-valued group, three-dimensional manifold",
author = "Buchstaber, {Victor M.} and Vesnin, {Andrei Yu}",
note = "Исследование В.М. Бухштабера выполнено в рамках проекта “Зеркальные лаборатории” НИУ ВШЭ. Исследование А.Ю. Веснина выполнено в рамках соглашения о зеркальных лабораториях при поддержке Программы развития НИ ТГУ (проект НУ 2.0.1.23 ОНТ Приоритет-2030).",
year = "2024",
doi = "10.4213/sm10089e",
language = "English",
volume = "215",
pages = "1441--1467",
journal = "Sbornik Mathematics",
issn = "1064-5616",
publisher = "Математический институт им. В.А. Стеклова Российской академии наук (Москва)",
number = "11",

}

RIS

TY - JOUR

T1 - n-valued groups, branched coverings and hyperbolic 3-manifolds

AU - Buchstaber, Victor M.

AU - Vesnin, Andrei Yu

N1 - Исследование В.М. Бухштабера выполнено в рамках проекта “Зеркальные лаборатории” НИУ ВШЭ. Исследование А.Ю. Веснина выполнено в рамках соглашения о зеркальных лабораториях при поддержке Программы развития НИ ТГУ (проект НУ 2.0.1.23 ОНТ Приоритет-2030).

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - Fibonacci group

KW - branched cyclic covering

KW - cyclically presented group

KW - knot

KW - n-valued group

KW - three-dimensional manifold

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UR - https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=10089&option_lang=rus

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U2 - 10.4213/sm10089e

DO - 10.4213/sm10089e

M3 - Article

VL - 215

SP - 1441

EP - 1467

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 11

ER -

ID: 64823603