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Cohomotopy invariants and the universal cohomotopy invariant jump formula
http://hdl.handle.net/2261/30797
http://hdl.handle.net/2261/30797eeff6959-06f7-422e-8f10-a0b8b09e800d
名前 / ファイル | ライセンス | アクション |
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jms150301.pdf (554.5 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2009-12-23 | |||||
タイトル | ||||||
タイトル | Cohomotopy invariants and the universal cohomotopy invariant jump formula | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
著者 |
Okonek, Christian
× Okonek, Christian× Teleman, Andrei |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | Starting from ideas of Furuta, we develop a general formalism for the construction of cohomotopy invariants associated with a certain class of $S^1$-equivariant non-linear maps between Hilbert bundles. Applied to the Seiberg-Witten map, this formalism yields a new class of cohomotopy Seiberg-Witten invariants which have clear functorial properties with respect to diffeomorphisms of 4-manifolds. Our invariants and the Bauer-Furuta classes are directly comparable for 4-manifolds with $b_1=0$; they are equivalent when $b_1=0$ and $b_+>1$, but are finer in the case $b_1=0$, $b_+=1$ (they detect the wall-crossing phenomena). We study fundamental properties of the new invariants in a very general framework. In particular we prove a universal cohomotopy invariant jump formula and a multiplicative property. The formalism applies to other gauge theoretical problems, e.g. to the theory of gauge theoretical (Hamiltonian) Gromov-Witten invariants | |||||
書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 15, 号 3, p. 325-409, 発行日 2008-12-22 |
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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 | |||||
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内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
日本十進分類法 | ||||||
主題Scheme | NDC | |||||
主題 | 415 | |||||
Mathmatical Subject Classification | ||||||
値 | 57R57(MSC2000) | |||||
Mathmatical Subject Classification | ||||||
値 | 55Q55(MSC2000) | |||||
出版者 | ||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
原稿受領日 | ||||||
値 | 2008-02-15 |