An SO(3)-monopole cobordism formula relating Donaldson and Seiberg-Witten invariants /
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| Author / Creator: | Feehan, Paul M. N., 1961- author. |
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| Imprint: | Providence, RI : American Mathematical Society, [2018] |
| Description: | xiv, 234 pages ; 26 cm |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society, 1947-6221 ; no. 1226 Memoirs of the American Mathematical Society ; no. 1226. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11751878 |
| Summary: | 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.<br> <br> 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. |
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| Physical Description: | xiv, 234 pages ; 26 cm |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781470414214 147041421X |
| ISSN: | 1947-6221 ; |
