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Theory of Fibered 3Knots in $S^5$ and its Applications
http://hdl.handle.net/2261/1232
ea1ba464312a456f847c7bc1e7d00612
名前 / ファイル  ライセンス  アクション  

jms060404.pdf (491.4 kB)


Item type  紀要論文 / Departmental Bulletin Paper(1)  

公開日  20080304  
タイトル  
タイトル  Theory of Fibered 3Knots in $S^5$ and its Applications  
言語  
言語  eng  
キーワード  
主題  Fibered knot  
主題Scheme  Other  
キーワード  
主題  Seifert matrix  
主題Scheme  Other  
資源タイプ  
資源  http://purl.org/coar/resource_type/c_6501  
タイプ  departmental bulletin paper  
著者 
Saeki, Osamu
× Saeki, Osamu 

抄録  
内容記述タイプ  Abstract  
内容記述  Let $K$ be a closed connected orientable 3manifold embedded in $S^5$ whose complement smoothly fibers over the circle with simply connected fibers. Such an embedded 3manifold is called a {\it simple fibered\/} 3{\it knot}. In this paper we study such embedded 3manifolds and give various new results, which are classified into three types: (1) those which are similar to higher dimensional fibered knots, (2) those which are peculiar to fibered knots in $S^5$, and (3) applications. Among the results of type (1) are the isotopy criterions via Seifert matrices, determining fibered 3knots by their exteriors, topological or stable uniqueness of the fibering structures, and the effectiveness of plumbing operations. As results of type (2), we give various explicit examples of fibered 3knots with the same diffeomorphism type of the abstract 3manifolds and with congruent Seifert matrices but with different isotopy types. We also give some examples of fibered knots whose exteriors are diffeomorphic but with different isotopy types. We also show that there exist infinitely many embeddings of the punctured K3 surface into $S^5$ which are fibers of topological fibrations but which can never be a fiber of any smooth fibrations. We construct a fibered 3knot which is decomposable as a knot such that neither of the factor knots are fibered. As a result of type (3), we study topological isotopies of homeomorphisms of simply connected 4manifolds with boundary by using the techniques of fibered 3knots. We also apply our techniques to the embedding problem of simply connected 4manifolds into $S^6$. Finally we give some applications to the topological study of isolated hypersurface singularities in ${\bf C}^3$.  
書誌情報 
Journal of mathematical sciences, the University of Tokyo 巻 6, 号 4, p. 691756, 発行日 1999 

ISSN  
収録物識別子タイプ  ISSN  
収録物識別子  13405705  
書誌レコードID  
収録物識別子タイプ  NCID  
収録物識別子  AA11021653  
フォーマット  
内容記述タイプ  Other  
内容記述  application/pdf  
日本十進分類法  
主題  415  
主題Scheme  NDC  
Mathematical Reviews Number  
MR1742599  
Mathmatical Subject Classification  
57Q45(MSC1991)  
Mathmatical Subject Classification  
57N35(MSC1991)  
出版者  
出版者  Graduate School of Mathematical Sciences, The University of Tokyo  
原稿受領日  
19990315 