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An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants.
・ISBN 978-1-4704-1421-4 paper US$ 78.00
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| 著者・編者 | Feehan, Paul / Leness, Thomas G., |
|---|---|
| シリーズ | Memoirs of the American Mathematical Society |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2019 |
| ページ数 | 228 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-13242＞ |
解説
The authors prove an analogue of the Kotschick-Morgan Conjecture in the context of $\mathrm{SO(3)}$ monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-manifolds using the $\mathrm{SO(3)}$-monopole cobordism. The main technical difficulty in the $\mathrm{SO(3)}$-monopole program relating the Seiberg-Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible $\mathrm{SO(3)}$ monopoles, namely the moduli spaces of Seiberg-Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of $\mathrm{SO(3)}$ monopoles.
In this monograph, the authors prove--modulo a gluing theorem which is an extension of their earlier work--that these intersection pairings can be expressed in terms of topological data and Seiberg-Witten invariants of the four-manifold. Their proofs that the $\mathrm{SO(3)}$-monopole cobordism yields both the Superconformal Simple Type Conjecture of Moore, Marino, and Peradze and Witten's Conjecture in full generality for all closed, oriented, smooth four-manifolds with $b_1=0$ and odd $b^+\ge 3$ appear in earlier works.
In this monograph, the authors prove--modulo a gluing theorem which is an extension of their earlier work--that these intersection pairings can be expressed in terms of topological data and Seiberg-Witten invariants of the four-manifold. Their proofs that the $\mathrm{SO(3)}$-monopole cobordism yields both the Superconformal Simple Type Conjecture of Moore, Marino, and Peradze and Witten's Conjecture in full generality for all closed, oriented, smooth four-manifolds with $b_1=0$ and odd $b^+\ge 3$ appear in earlier works.