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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2015

Some hyperbolic three-manifolds that bound geometrically

Résumé

A closed connected hyperbolic n-manifold bounds geometrically if it is isometric to the geodesic boundary of a compact hyperbolic (n + 1)-manifold. A. Reid and D. Long have shown by arithmetic methods the existence of infinitely many manifolds that bound geometrically in every dimension. We construct here infinitely many explicit examples in dimension n = 3 using right-angled dodecahedra and 120-cells and a simple colouring technique introduced by M. Davis and T. Januszkiewicz. Namely, for every k 1, we build an orientable compact closed 3-manifold tessellated by 16k right-angled dodecahedra that bounds a 4-manifold tessellated by 32k right-angled 120-cells. A notable feature of this family is that the ratio between the volumes of the 4-manifolds and their boundary components is constant and, in particular, bounded.
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Dates et versions

hal-01287540 , version 1 (13-03-2016)
hal-01287540 , version 2 (24-06-2020)

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Alexander Kolpakov, Bruno Martelli, Steven Tschantz. Some hyperbolic three-manifolds that bound geometrically. Proceedings of the American Mathematical Society, 2015, 143, pp.4103-4111. ⟨10.1090/proc/12520⟩. ⟨hal-01287540v2⟩

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