| eBook ISBN: | 978-1-4704-4915-5 |
| Product Code: | MEMO/256/1226.E |
| List Price: | $78.00 |
| MAA Member Price: | $70.20 |
| AMS Member Price: | $46.80 |
| eBook ISBN: | 978-1-4704-4915-5 |
| Product Code: | MEMO/256/1226.E |
| List Price: | $78.00 |
| MAA Member Price: | $70.20 |
| AMS Member Price: | $46.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 256; 2018; 228 ppMSC: Primary 57; 58; Secondary 53
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, Mariño, 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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Table of Contents
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Chapters
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Preface
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1. Introduction
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2. Preliminaries
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3. Diagonals of symmetric products of manifolds
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4. A partial Thom–Mather structure on symmetric products
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5. The instanton moduli space with spliced ends
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6. The space of global splicing data
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7. Obstruction bundle
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8. Link of an ideal Seiberg–Witten moduli space
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9. Cohomology and duality
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10. Computation of the intersection numbers
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11. Kotschick–Morgan Conjecture
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Glossary of Notation
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Additional Material
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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, Mariño, 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.
-
Chapters
-
Preface
-
1. Introduction
-
2. Preliminaries
-
3. Diagonals of symmetric products of manifolds
-
4. A partial Thom–Mather structure on symmetric products
-
5. The instanton moduli space with spliced ends
-
6. The space of global splicing data
-
7. Obstruction bundle
-
8. Link of an ideal Seiberg–Witten moduli space
-
9. Cohomology and duality
-
10. Computation of the intersection numbers
-
11. Kotschick–Morgan Conjecture
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Glossary of Notation
