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On the Vanishing of the Rokhlin Invariant
http://hdl.handle.net/2261/52707
http://hdl.handle.net/2261/52707cf207227-275a-4f29-a36f-87e9270529d3
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms180205.pdf (232.5 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 公開日 | 2012-12-12 | |||||
| タイトル | ||||||
| タイトル | On the Vanishing of the Rokhlin Invariant | |||||
| 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 | It is a natural consequence of fundamental properties of the Casson invariant that the Rokhlin invariant μ(M) of an amphichiral integral homology 3-sphere M vanishes. In this paper, we give a new direct proof of this vanishing property. For such an M, we construct a manifold pair (Y, Q) of dimensions 6 and 3 equipped with some additional structure (6-dimensional spin e-manifold), such that Q ≅ M ∐ M ∐ (-M), and (Y, Q) ≅ (-Y, -Q). We prove that (Y, Q) bounds a 7-dimensional spin e-manifold (Z, X) by studying the cobordism group of 6-dimensional spin e-manifolds and the Z/2-action on the two-point configuration space of M \ {pt}. For any such (Z, X), the signature of X vanishes, and this implies μ(M) = 0. The idea of the construction of (Y, Q) comes from the definition of the Kontsevich-Kuperberg-Thurston invariant for rational homology 3-spheres. | |||||
| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 18, 号 2, p. 239-268, 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 | ||||||
| 57M27(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 57N70(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 57R20(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 55R80(MSC2010) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 2011-05-19 | ||||||
