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Russian Mathematical Surveys, 2017, Volume 72, Issue 2, Pages 335–374
DOI: https://doi.org/10.1070/RM9762
(Mi rm9762)
 

This article is cited in 19 scientific papers (total in 20 papers)

Right-angled polyhedra and hyperbolic 3-manifolds

A. Yu. Vesnin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
References:
Abstract: Hyperbolic 3-manifolds whose fundamental groups are subgroups of finite index in right-angled Coxeter groups are under consideration. The construction of such manifolds is associated with of the faces of polyhedra and, in particular, with 4-colourings. The following questions are discussed: the structure of the set of right-angled polytopes in Lobachevskii space; examples of orientable and non-orientable manifolds, including the classical Löbell manifold constructed in 1931; connections between the Hamiltonian property of a polyhedron and the existence of hyperelliptic involutions of manifolds; the volumes and complexity of manifolds; isometry between hyperbolic manifolds constructed from 4-colourings.
Bibliography: 89 titles.
Keywords: right-angled reflection groups, hyperbolic 3-manifolds, volumes of manifolds, colourings of polyhedra, Hamiltonian graphs, small covers.
Funding agency Grant number
Russian Science Foundation 16-41-02006
This research was supported by the Russian Science Foundation (grant no. 16-41-02006).
Received: 31.01.2017
Revised: 16.02.2017
Russian version:
Uspekhi Matematicheskikh Nauk, 2017, Volume 72, Issue 2(434), Pages 147–190
DOI: https://doi.org/10.4213/rm9762
Bibliographic databases:
Document Type: Article
UDC: 514.132+515.162
MSC: Primary 52B10, 52B11, 57N10; Secondary 22E40, 51M10
Language: English
Original paper language: Russian
Citation: A. Yu. Vesnin, “Right-angled polyhedra and hyperbolic 3-manifolds”, Uspekhi Mat. Nauk, 72:2(434) (2017), 147–190; Russian Math. Surveys, 72:2 (2017), 335–374
Citation in format AMSBIB
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  • https://doi.org/10.1070/RM9762
  • https://www.mathnet.ru/eng/rm/v72/i2/p147
  • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Успехи математических наук Russian Mathematical Surveys
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    Russian version PDF:355
    English version PDF:35
    References:93
    First page:52
     
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