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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Spherical 3-manifold ： ウィキペディア英語版 Spherical 3-manifold In mathematics, a spherical 3-manifold ''M'' is a 3-manifold of the form :$M=S^3/\backslash Gamma$ where $\backslash Gamma$ is a finite subgroup of SO(4) acting freely by rotations on the 3-sphere $S^3$. All such manifolds are prime, orientable, and closed. Spherical 3-manifolds are sometimes called elliptic 3-manifolds or Clifford-Klein manifolds. ==Properties== A spherical 3-manifold has a finite fundamental group isomorphic to Γ itself. The elliptization conjecture, proved by Grigori Perelman, states that conversely all 3-manifolds with finite fundamental group are spherical manifolds. The fundamental group is either cyclic, or is a central extension of a dihedral, tetrahedral, octahedral, or icosahedral group by a cyclic group of even order. This divides the set of such manifolds into 5 classes, described in the following sections. The spherical manifolds are exactly the manifolds with spherical geometry, one of the 8 geometries of Thurston's geometrization conjecture. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Spherical 3-manifold」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.