翻訳と辞書 Words near each other ・ "O" Is for Outlaw ・ "O"-Jung.Ban.Hap. ・ "Ode-to-Napoleon" hexachord ・ "Oh Yeah!" Live ・ "Our Contemporary" regional art exhibition (Leningrad, 1975) ・ "P" Is for Peril ・ "Pimpernel" Smith ・ "Polish death camp" controversy ・ "Pro knigi" ("About books") ・ "Prosopa" Greek Television Awards ・ "Pussy Cats" Starring the Walkmen ・ "Q" Is for Quarry ・ "R" Is for Ricochet ・ "R" The King (2016 film) ・ "Rags" Ragland ・ ! (album) ・ ! (disambiguation) ・ !! ・ !!! ・ !!! (album) ・ !!Destroy-Oh-Boy!! ・ !Action Pact! ・ !Arriba! La Pachanga ・ !Hero ・ !Hero (album) ・ !Kung language ・ !Oka Tokat ・ !PAUS3 ・ !T.O.O.H.! ・ !Women Art Revolution Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク lens space ： ウィキペディア英語版 lens space A lens space is an example of a topological space, considered in mathematics. The term often refers to a specific class of 3-manifolds, but in general can be defined for higher dimensions. In the 3-manifold case, a lens space can be visualized as the result of gluing two solid tori together by a homeomorphism of their boundaries. Often the 3-sphere and $S^2\; \backslash times\; S^1$, both of which can be obtained as above, are not counted as they are considered trivial special cases. The three-dimensional lens spaces $L(p,q)$ were introduced by Tietze in 1908. They were the first known examples of 3-manifolds which were not determined by their homology and fundamental group alone, and the simplest examples of closed manifolds whose homeomorphism type is not determined by their homotopy type. J.W. Alexander in 1919 showed that the lens spaces $L(5;1)$ and $L(5;2)$ were not homeomorphic even though they have isomorphic fundamental groups and the same homology, though they do not have the same homotopy type. Other lens spaces have even the same homotopy type (and thus isomorphic fundamental groups and homology), but not the same homeomorphism type; they can thus be seen as the birth of geometric topology of manifolds as distinct from algebraic topology. There is a complete classification of three-dimensional lens spaces, by fundamental group and Reidemeister torsion. == Definition == The three-dimensional lens spaces $L(p;q)$ are quotients of $S^3$ by $\backslash mathbb/p$-actions. More precisely, let $p$ and $q$ be coprime integers and consider $S^3$ as the unit sphere in $\backslash mathbb\; C^2$. Then the $\backslash mathbb/p$-action on $S^3$ generated by :$().(z\_1,z\_2):=(e^\; \backslash cdot\; z\_1,\; e^\backslash cdot\; z\_2)$ is free as p and q were coprime. The resulting quotient space is called the lens space $L(p;q)$. This can be generalized to higher dimensions as follows: Let $p,q\_1,\backslash ldots,q\_n$ be integers such that the $q\_i$ are coprime to $p$ and consider $S^$ as the unit sphere in $\backslash mathbb\; C^n$. The lens space $L(p;q\_1,\backslash ldots\; q\_n)$ is the quotient of $S^$ by the free $\backslash mathbb\; Z/p$-action generated by :$().(z\_1,\backslash ldots,z\_n):=(e^\; \backslash cdot\; z\_1,\backslash ldots,\; e^\backslash cdot\; z\_n).$ In three dimensions we have $L(p;q)=L(p;1,q).$ The fundamental group of all the lens spaces $L(p;q\_1,\backslash ldots,\; q\_n)$ is $\backslash mathbb\; Z/p$ independent of the $q\_i$. 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「lens space」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.