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An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants
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(...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2019.
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| Colección: | Memoirs of the American Mathematical Society Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Mu 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_on1083465463 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr |n|---||||| | ||
| 008 | 190126s2019 riu o 000 0 eng d | ||
| 040 | |a EBLCP |b eng |e pn |c EBLCP |d OCLCQ |d LOA |d OCLCO |d OCLCF |d K6U |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 020 | |a 9781470449155 | ||
| 020 | |a 1470449153 | ||
| 029 | 1 | |a AU@ |b 000069468752 | |
| 035 | |a (OCoLC)1083465463 | ||
| 050 | 4 | |a QA613.66 |b .F444 2018 | |
| 082 | 0 | 4 | |a 514.72 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Feehan, Paul. | |
| 245 | 1 | 3 | |a An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants |
| 260 | |a Providence : |b American Mathematical Society, |c 2019. | ||
| 300 | |a 1 online resource (254 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society Ser. ; |v v. 256 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Title page; Preface; Acknowledgments; Chapter 1. Introduction; 1.1. Summary of main results; 1.2. Outline of the argument; 1.2.1. Problem of overlaps; 1.2.2. Overlap space and overlap maps; 1.2.3. Associativity of splicing maps; 1.2.4. Instanton moduli space with spliced ends; 1.2.5. Space of global splicing data; 1.2.6. Definition of link of a subspace of a moduli space of ideal Seiberg-Witten monopoles; 1.2.7. Computation of intersection numbers with the link of the moduli space of ideal Seiberg-Witten monopoles; 1.3. Kotschick-Morgan Conjecture; 1.4. Outline of the monograph | |
| 505 | 8 | |a Chapter 2. Preliminaries2.1. The moduli space of \SO(3) monopoles; 2.1.1. Clifford modules; 2.1.2. \SO(3) monopoles; 2.2. Stratum of anti-self-dual or zero-section solutions; 2.3. Strata of Seiberg-Witten or reducible solutions; 2.3.1. Seiberg-Witten monopoles; 2.3.2. Seiberg-Witten invariants; 2.3.3. Reducible \SO(3) monopoles; 2.3.4. Circle actions; 2.3.5. The virtual normal bundle of the Seiberg-Witten moduli space; 2.4. Cohomology classes on the moduli space of \SO(3) monopoles; 2.5. Donaldson invariants; 2.6. Links and the cobordism | |
| 505 | 8 | |a Chapter 3. Diagonals of symmetric products of manifolds3.1. Definitions; 3.1.1. Subgroups of the symmetric group; 3.1.2. Definition of the diagonals; 3.1.3. Strata of the symmetric product; 3.2. Incidence relations among diagonals and strata; 3.3. Normal bundles of diagonals and strata; 3.4. Enumeration of the strata; Chapter 4. A partial Thom-Mather structure on symmetric products; 4.1. Introduction; 4.2. Diagonals in products of \RR⁴; 4.3. Families of metrics; 4.4. Overlap maps; 4.4.1. The downwards overlap map; 4.4.2. The upwards overlap map; 4.4.3. Commuting overlap maps | |
| 505 | 8 | |a 4.4.4. The projection maps4.5. Construction of the families of locally flattened metrics; 4.6. Normal bundles of strata of \Sym^{ℓ}(); 4.7. The tubular distance function; 4.8. Decomposition of the strata; Chapter 5. The instanton moduli space with spliced ends; 5.1. Introduction; 5.2. Connections over the four-dimensional sphere; 5.3. Strata containing the product connection; 5.3.1. Tubular neighborhoods; 5.4. The splicing map with the product connection over \RR⁴; 5.5. Composition of splicing maps; 5.5.1. Definition of the overlap data; 5.5.2. Equality of splicing maps | |
| 505 | 8 | |a 5.5.3. Symmetric group actions and quotients5.6. The spliced end of the instanton moduli space; 5.7. Tubular neighborhoods of the instanton moduli space with spliced ends; 5.8. Isotopy of the spliced end of the instanton moduli space; 5.9. Properties of the instanton moduli space with spliced ends; Chapter 6. The space of global splicing data; 6.1. Introduction; 6.2. Splicing data; 6.2.1. Background pairs; 6.2.2. Riemannian metrics; 6.2.3. Frame bundles; 6.2.4. Group actions on the frame bundles; 6.2.5. Space of splicing data; 6.3. The flattening map on pairs; 6.4. The crude splicing map | |
| 500 | |a 6.4.1. The standard splicing map | ||
| 520 | |a 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 modu. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Cobordism theory. | |
| 650 | 0 | |a Four-manifolds (Topology) | |
| 650 | 0 | |a Seiberg-Witten invariants. | |
| 650 | 6 | |a Théorie des cobordismes. | |
| 650 | 6 | |a Variétés topologiques à 4 dimensions. | |
| 650 | 6 | |a Invariants de Seiberg-Witten. | |
| 650 | 7 | |a Cobordism theory |2 fast | |
| 650 | 7 | |a Four-manifolds (Topology) |2 fast | |
| 650 | 7 | |a Seiberg-Witten invariants |2 fast | |
| 700 | 1 | |a Leness, Thomas G. | |
| 758 | |i has work: |a An SO(3)-monopole cobordism formula relating Donaldson and Seiberg-Witten invariants (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGkB778yqkQxgYFhMBbWXd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Feehan, Paul. |t An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants. |d Providence : American Mathematical Society, ©2019 |
| 830 | 0 | |a Memoirs of the American Mathematical Society Ser. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5633663 |z Texto completo |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5633663 | ||
| 994 | |a 92 |b IZTAP | ||