An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants. (Record no. 7633)
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| control field | EBC5633663 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724113522.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
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| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2019 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470449155 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470414214 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5633663 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5633663 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1083465463 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA613.66 .F444 2018 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 514.72 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Feehan, Paul. |
| 245 13 - TITLE STATEMENT | |
| Title | An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2019. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2018. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (254 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.256 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 -- Chapter 2. Preliminaries -- 2.1. 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 -- Chapter 3. Diagonals of symmetric products of manifolds -- 3.1. 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 -- 4.4.4. The projection maps. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 4.5. 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 -- 5.5.3. Symmetric group actions and quotients -- 5.6. 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 -- 6.4.1. The standard splicing map -- 6.4.2. Construction of the crude splicing map -- 6.4.3. Properties of the crude splicing map -- 6.5. Overlap spaces and maps -- 6.5.1. The overlap space -- 6.5.2. The upwards overlap map -- 6.5.3. Downwards overlap map -- 6.5.4. Equality of splicing maps -- 6.6. Construction of the space of global splicing data -- 6.7. Thom-Mather structures on the space of global splicing data -- 6.8. Global splicing map -- 6.9. Projections onto symmetric products -- Chapter 7. Obstruction bundle -- 7.1. Introduction -- 7.2. Infinite-rank obstruction pseudo-bundle -- 7.3. Background obstruction bundle -- 7.4. Equivariant Dirac index bundle. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 7.5. The action of \Spinu(4) -- 7.6. Pseudo-bundle over the instanton moduli space with spliced ends -- 7.6.1. Pseudo-bundles and overlap data -- 7.7. Instanton obstruction pseudo-bundle -- 7.7.1. The frame bundles -- 7.7.2. Splicing map -- 7.7.3. Overlap space and overlap maps -- 7.8. Local gluing hypothesis for \SO(3) monopoles -- 7.9. Notes on the justification of the local gluing hypothesis -- 7.9.1. Construction of a virtual neighborhood for the moduli space of \SO(3) monopoles near a top-level singular stratum of \SO(3) monopoles -- 7.9.2. Virtual neighborhoods for the moduli space of anti-self-dual connections -- 7.9.3. Extrinsic virtual neighborhoods for the moduli space of anti-self-dual connections and gluing -- 7.9.4. Construction of a virtual neighborhood for the moduli space of \SO(3) monopoles near a lower-level singular stratum of \SO(3) monopoles -- Chapter 8. Link of an ideal Seiberg-Witten moduli space -- 8.1. Definition of the link of an ideal Seiberg-Witten moduli space -- 8.1.1. The virtual link of an ideal Seiberg-Witten moduli space -- 8.1.2. The link of an ideal Seiberg-Witten moduli space -- 8.1.3. A subspace of the virtual link of an ideal Seiberg-Witten moduli space -- 8.1.4. Orientations of the link of an ideal Seiberg-Witten moduli space -- 8.1.5. An equality of intersection numbers provided by the \SO(3)-monopole cobordism -- 8.2. Fiber bundle structure of the instanton component of the link of an ideal Seiberg-Witten moduli space -- 8.3. Boundaries of components of links of ideal Seiberg-Witten moduli spaces -- Chapter 9. Cohomology and duality -- 9.1. Introduction -- 9.2. Definitions -- 9.2.1. Subspaces and maps -- 9.2.2. The incidence locus -- 9.2.3. Cohomology classes -- 9.3. Fundamental class of the virtual link of the ideal moduli space of Seiberg-Witten monopoles -- 9.4. Computation of the -classes. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 9.4.1. Geometric representatives and cocycles -- 9.4.2. Cocycles as pullbacks -- 9.4.3. Computations of cocycles -- 9.5. Relative Euler class of the obstruction pseudo-bundle -- 9.5.1. Euler class of the Seiberg-Witten component of the obstruction pseudo-bundle -- 9.5.2. Local Euler class of the instanton component of the obstruction bundle -- 9.5.3. Global Euler class of the instanton component of the obstruction bundle -- 9.5.4. Relative Euler classes -- 9.6. Duality and the link of an ideal Seiberg-Witten moduli space -- 9.6.1. The initial duality -- 9.6.2. Extension of the cocycles -- 9.7. Reduction to the subspace \bB\bL^{\vir}_{\ft,\fs} -- Chapter 10. Computation of the intersection numbers -- 10.1. Introduction -- 10.2. Quotient space of \bB\bL^{\vir}_{\ft,\fs} -- 10.2.1. Quotient maps -- 10.2.2. Construction of the local quotient -- 10.2.3. Global quotient of \bB\bL^{\vir}_{\ft,\fs} -- 10.3. Homology and cohomology classes of the quotient -- 10.4. Fiber bundles and pushforwards -- 10.5. Computations of intersection numbers on \bL_{\ft,\fs} -- 10.6. Proofs of the main theorems -- Chapter 11. Kotschick-Morgan Conjecture -- 11.1. Cobordisms and reducible connections -- 11.2. Cohomology classes on the cobordism -- 11.3. Neighborhoods of gauge-equivalence classes of ideal reducible connections -- 11.3.1. Kuranishi model for a neighborhood of a reducible connection -- 11.3.2. Crude splicing maps -- 11.3.3. Overlap spaces and maps -- 11.3.4. Definition of the neighborhood of a gauge-equivalence class of an ideal reducible connection -- 11.3.5. Thom-Mather structures on ̃\sU^{ }_{\ka}( )/ ¹ -- 11.3.6. Global projection map for ̃\sU^{ }_{\ka}( )/ ¹ -- 11.3.7. Global splicing map on ̃\sU^{ }_{\ka}( )/ ¹ -- 11.3.8. Obstruction bundle on ̃\sU^{ }_{\ka}( )/ ¹ -- 11.3.9. Gluing hypothesis -- 11.4. Cohomology classes on the space of global splicing data. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 11.5. Definition of the link of a gauge-equivalence class of an ideal reducible connection -- 11.6. Computations of the difference term -- Glossary of Notation -- Bibliography -- Index -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Cobordism theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Four-manifolds (Topology). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Seiberg-Witten invariants. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Leness, Thomas G. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Feehan, Paul |
| Title | An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2019 |
| International Standard Book Number | 9781470414214 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5633663">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5633663</a> |
| Public note | Click to View |
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