An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-1421-4 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-1421-4 (ISBN)
- Titel z.Zt. nicht lieferbar
- Versandkostenfrei
- Auch auf Rechnung
- Artikel merken
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.
Paul Feehan, Rutgers, The State University of New Jersey, Piscataway, NJ. Thomas G. Leness, Florida International University, Miami, FL.
Preface
Introduction
Preliminaries
Diagonals of symmetric products of manifolds
A partial Thom-Mather structure on symmetric products
The instanton moduli space with spliced ends
The space of global splicing data
Obstruction bundle
Link of an ideal Seiberg-Witten moduli space
Cohomology and duality
Computation of the intersection numbers
Kotschick-Morgan Conjecture
Glossary of Notation
Index
Bibliography.
| Erscheinungsdatum | 20.02.2019 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 365 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-4704-1421-X / 147041421X |
| ISBN-13 | 978-1-4704-1421-4 / 9781470414214 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Gekrümmte Kurven und Flächen
Buch | Softcover (2024)
De Gruyter (Verlag)
CHF 76,90
a history of modern trigonometry
Buch | Softcover (2025)
Princeton University Press (Verlag)
CHF 34,90
