The problem of classifying, up to isometry, the orientable 3-manifolds that arise by identifying the faces of a Platonic solid was completely solved in a nice paper of Everitt [B. Everitt, 3-manifolds from Platonic solids, Topology Appl. 138 (2004) 253–263]. His work completes the classification begun by Best [L.A. Best, On torsion-free discrete subgroups of PSL_2(C) with compact orbit space, Canad. J. Math. 23 (1971) 451–460],Lorimer [P.J. Lorimer, Four dodecahedral spaces, Pacific J. Math. 156 (2) (1992) 329–335], Prok [I. Prok, Classification of dodecahedral space forms, Beiträge Algebra Geom. 39 (2)(1998) 497–515], and Richardson and Rubinstein [J. Richardson, J.H. Rubinstein, Hyperbolic manifolds from a regular polyhedron, Preprint]. In this paper we investigate the topology of closed orientable 3-manifolds from Platonic solids. Here we completely recognize those manifolds in the spherical and Euclidean cases, and state topological properties for many of them in the hyperbolic case. The proofs of the latter will appear in a forthcoming paper.

Topology of compact space forms from Platonic solids. I / Cavicchioli, Alberto; Spaggiari, Fulvia; Telloni, Agnese Ilaria. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 156:4(2009), pp. 812-822. [10.1016/j.topol.2008.10.015]

Topology of compact space forms from Platonic solids. I.

CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia;TELLONI, Agnese Ilaria
2009

Abstract

The problem of classifying, up to isometry, the orientable 3-manifolds that arise by identifying the faces of a Platonic solid was completely solved in a nice paper of Everitt [B. Everitt, 3-manifolds from Platonic solids, Topology Appl. 138 (2004) 253–263]. His work completes the classification begun by Best [L.A. Best, On torsion-free discrete subgroups of PSL_2(C) with compact orbit space, Canad. J. Math. 23 (1971) 451–460],Lorimer [P.J. Lorimer, Four dodecahedral spaces, Pacific J. Math. 156 (2) (1992) 329–335], Prok [I. Prok, Classification of dodecahedral space forms, Beiträge Algebra Geom. 39 (2)(1998) 497–515], and Richardson and Rubinstein [J. Richardson, J.H. Rubinstein, Hyperbolic manifolds from a regular polyhedron, Preprint]. In this paper we investigate the topology of closed orientable 3-manifolds from Platonic solids. Here we completely recognize those manifolds in the spherical and Euclidean cases, and state topological properties for many of them in the hyperbolic case. The proofs of the latter will appear in a forthcoming paper.
2009
156
4
812
822
Topology of compact space forms from Platonic solids. I / Cavicchioli, Alberto; Spaggiari, Fulvia; Telloni, Agnese Ilaria. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 156:4(2009), pp. 812-822. [10.1016/j.topol.2008.10.015]
Cavicchioli, Alberto; Spaggiari, Fulvia; Telloni, Agnese Ilaria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/594024
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