Right-angled polyhedra and hyperbolic 3-manifolds

A. Yu. Vesnin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 72 (2017) no. 2, pp. 335-374

Résumé

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.

Détail

Keywords: right-angled reflection groups, hyperbolic 3-manifolds, volumes of manifolds, colourings of polyhedra, Hamiltonian graphs, small covers.

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