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An Invariant of Embeddings of 3-Manifolds in 6-Manifolds and Milnor's Triple Linking Number
http://hdl.handle.net/2261/52706
http://hdl.handle.net/2261/5270637ef7982-8b2a-414f-8e95-6864bcafa887
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms180204.pdf (309.7 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2012-12-12 | |||||
| タイトル | ||||||
| タイトル | An Invariant of Embeddings of 3-Manifolds in 6-Manifolds and Milnor's Triple Linking Number | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Moriyama, Tetsuhiro
× Moriyama, Tetsuhiro |
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| 著者所属 | ||||||
| 著者所属 | Shibano Patent Office | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | We give a simple axiomatic definition of a rational-valued invariant σ(W, V, e) of triples (W, V, e), where W ⊃ V are smooth oriented closed manifolds of dimensions 6 and 3, and e is a second rational cohomology class of the complement W \ V satisfying a certain condition. The definition is stated in terms of cobordisms of such triples and the signature of 4-manifolds. When W = S6 and V is a smoothly embedded 3-sphere, and when e/2 is the Poincaré dual of a Seifert surface of V, the invariant coincides with -8 times Haefliger's embedding invariant of (S6, V). Our definition recovers a more general invariant due to Takase, and contains a new definition for Milnor's triple linking number of algebraically split 3-component links in R3 that is close to the one given by the perturbative series expansion of the Chern-Simons theory of links in R3. | |||||
| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 18, 号 2, p. 193-237, 発行日 2011-12-09 |
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| 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 | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 415 | |||||
| Mathematical Reviews Number | ||||||
| MR | ||||||
| Mathmatical Subject Classification | ||||||
| 57R40(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 57M27(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 57R52(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 57M25(MSC2010) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 2011-05-09 | ||||||
