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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
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.
Received: 31.01.2017 Revised: 16.02.2017
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
Linking options:
https://www.mathnet.ru/eng/rm9762https://doi.org/10.1070/RM9762 https://www.mathnet.ru/eng/rm/v72/i2/p147
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Abstract page: | 1122 | Russian version PDF: | 355 | English version PDF: | 35 | References: | 93 | First page: | 52 |
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