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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 Trigenus ： ウィキペディア英語版 Trigenus In low-dimensional topology, the trigenus of a closed 3-manifold is an invariant consisting of an ordered triple $(g\_1,g\_2,g\_3)$. It is obtained by minimizing the genera of three ''orientable'' handle bodies — with no intersection between their interiors— which decompose the manifold as far as the Heegaard genus need only two. That is, a decomposition $M=V\_1\backslash cup\; V\_2\backslash cup\; V\_3$ with $V\_i\backslash cap\; V\_j=\backslash varnothing$ for $i,j=1,2,3$ and being $g\_i$ the genus of $V\_i$. For orientable spaces, $(M)=(0,0,h)$, where $h$ is $M$'s Heegaard genus. For non-orientable spaces the $$ has the form $(M)=(0,g\_2,g\_3)\backslash quad\; \backslash mbox\backslash quad\; (1,g\_2,g\_3)$ depending on the image of the first Stiefel–Whitney characteristic class $w\_1$ under a Bockstein homomorphism, respectively for $\backslash beta(w\_1)=0\backslash quad\; \backslash mbox\backslash quad\; \backslash neq\; 0.$ It has been proved that the number $g\_2$ has a relation with the concept of Stiefel–Whitney surface, that is, an orientable surface $G$ which is embedded in $M$, has minimal genus and represents the first Stiefel–Whitney class under the duality map $D\backslash colon\; H^1(M;\}\_2),$, that is, $Dw\_1(M)=()$. If $\backslash beta(w\_1)=0\; \backslash ,$ then $(M)=(0,2g,g\_3)\; \backslash ,$, and if $\backslash beta(w\_1)\backslash neq\; 0.\; \backslash ,$ then $(M)=(1,2g-1,g\_3)\; \backslash ,$. ==Theorem== A manifold ''S'' is a Stiefel–Whitney surface in ''M'', if and only if ''S'' and ''M−int(N(S))'' are orientable . 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「Trigenus」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.