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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 |
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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 | 415 | |||||
主題Scheme | NDC | |||||
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 |