Seifert fibrations of lens spaces
Seifert fibrations of lens spaces
复制标题
晶状体空间的 Seifert 纤维振动
DOI：
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复制
发表时间：
2016
影响因子：
0.4
通讯作者：
Christian Lange
中科院分区：
文献类型：
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作者：
H. Geiges;Christian Lange
我们对任意给定透镜空间L（p, q）的Seifert振动进行分类。从任意一对{素数}非零整数α10，α20documentclass[12pt]{minimal} usepackageamsmath{ useppackageamsfonts} useppackageamssymb{ useppackageamssy} useppackageamsfs{ setlengththoddsidemargin} -69pt{ }egindocument{}{}{}{}{}$$alpha _1^0,alpha _2^0$$ enddocument，{我们给出}了一种构造一个Seifert纤维的算法L（p,q）→S2(α|α10|,α|α20|)documentclass[12pt]minimal {usepackageamsmath} useppackageamsfonts{ useppackageamssymb} useppackageamssy{ useppackageamsfs} setlengththoddsidemargin{ -69pt} egindocument {}{}{}{}{}{}{}$$L(p,q)
ightarrow S^2(alpha |alpha _1^0|,alpha |alpha _2^0|)$$ enddocument，{其中}自然数αdocumentclass{[12pt]minimal} useppackageamsmath useppackagewasysym {useppackageamsfonts} useppackageamssyb{ useppackageamssy} useppackageamsfs{ useppackageupgreek }setlengthoddsidemargin{-}69pt egindocument {}{}{}{}{}{}$$alpha $$ enddocument{由算法}确定。该算法产生了所有可能的塞弗特纤维，并完整地描述了所产生的塞弗特纤维之间的同构性。此外，我们还证明了所有的Seifert颤振对某些标准模型都是同构的。
We classify the Seifert fibrations of any given lens space L(p, q). Starting from any pair of coprime non-zero integers α10,α20documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$alpha _1^0,alpha _2^0$$end{document}, we give an algorithmic construction of a Seifert fibration L(p,q)→S2(α|α10|,α|α20|)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L(p,q)
ightarrow S^2(alpha |alpha _1^0|,alpha |alpha _2^0|)$$end{document}, where the natural number αdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$alpha $$end{document} is determined by the algorithm. This algorithm produces all possible Seifert fibrations, and the isomorphisms between the resulting Seifert fibrations are described completely. Also, we show that all Seifert fibrations are isomorphic to certain standard models.