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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 Complex projective plane ： ウィキペディア英語版 Complex projective plane In mathematics, the complex projective plane, usually denoted P2(C), is the two-dimensional complex projective space. It is a complex manifold described by three complex coordinates :$(z\_1,z\_2,z\_3)\; \backslash in\; \backslash mathbf^3,\backslash qquad\; (z\_1,z\_2,z\_3)\backslash neq\; (0,0,0)$ where, however, the triples differing by an overall rescaling are identified: :$(z\_1,z\_2,z\_3)\; \backslash equiv\; (\backslash lambda\; z\_1,\backslash lambda\; z\_2,\; \backslash lambda\; z\_3);\backslash quad\; \backslash lambda\backslash in\; \backslash mathbf,\backslash qquad\; \backslash lambda\; \backslash neq\; 0.$ That is, these are homogeneous coordinates in the traditional sense of projective geometry. ==Topology== The Betti numbers of the complex projective plane are :1, 0, 1, 0, 1, 0, 0, ..... The middle dimension 2 is accounted for by the homology class of the complex projective line, or Riemann sphere, lying in the plane. The nontrivial homotopy groups of the complex projective plane are $\backslash pi\_2=\backslash pi\_5=\backslash mathbb$. The fundamental group is trivial and all other higher homotopy groups are those of the 5-sphere, i.e. torsion. 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「Complex projective plane」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.