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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 plus construction ： ウィキペディア英語版 plus construction In mathematics, the plus construction is a method for simplifying the fundamental group of a space without changing its homology and cohomology groups. It was introduced by , and was used by Daniel Quillen to define algebraic K-theory. Given a perfect normal subgroup of the fundamental group of a connected CW complex $X$, attach two-cells along loops in $X$ whose images in the fundamental group generate the subgroup. This operation generally changes the homology of the space, but these changes can be reversed by the addition of three-cells. The most common application of the plus construction is in algebraic K-theory. If $R$ is a unital ring, we denote by $GL\_n(R)$ the group of invertible $n$-by-$n$ matrices with elements in $R$. $GL\_n(R)$ embeds in $GL\_(R)$ by attaching a $1$ along the diagonal and $0$s elsewhere. The direct limit of these groups via these maps is denoted $GL(R)$ and its classifying space is denoted $BGL(R)$. The plus construction may then be applied to the perfect normal subgroup $E(R)$ of $GL(R)\; =\; \backslash pi\_1(BGL(R))$, generated by matrices which only differ from the identity matrix in one off-diagonal entry. For $i>0$, the $n$th homotopy group of the resulting space, $BGL(R)^+$ is the $n$th $K$-group of $R$, $K\_n(R)$. == See also == * Semi-s-cobordism 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「plus construction」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.