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.
Domaines
Géométrie métrique [math.MG]
Origine : Fichiers produits par l'(les) auteur(s)
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