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Floer homology groups in Yang-Mills theory / / S.K. Donaldson with the assistance of M. Furuta and D. Kotschick
| Floer homology groups in Yang-Mills theory / / S.K. Donaldson with the assistance of M. Furuta and D. Kotschick |
| Autore | Donaldson S. K |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Cambridge ; ; New York, : Cambridge University Press, 2002 |
| Descrizione fisica | 1 online resource (vii, 236 pages) : digital, PDF file(s) |
| Disciplina | 530.14/35 |
| Altri autori (Persone) |
FurutaM
KotschickD |
| Collana | Cambridge tracts in mathematics |
| Soggetto topico |
Yang-Mills theory
Geometry, Differential |
| ISBN |
1-107-12463-8
1-280-43046-X 9786610430468 0-511-17547-7 0-511-15583-2 0-511-30404-8 0-511-54309-3 0-511-04453-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Yang-Mills theory over compact manifolds -- The case of a compact 4-manifold -- Technical results -- Manifolds with tubular ends -- Yang-Mills theory and 3-manifolds -- Initial discussion -- The Chern-Simons functional -- The instanton equation -- Linear operators -- Appendix A: local models -- Appendix B: pseudo-holomorphic maps -- Appendix C: relations with mechanics -- Linear analysis -- Separation of variables -- Sobolev spaces on tubes -- Remarks on other operators -- The addition property -- Weighted spaces -- Floer's grading function; relation with the Atiyah, Patodi, Singer theory -- Refinement of weighted theory -- L[superscript p] theory -- Gauge theory and tubular ends -- Exponential decay -- Moduli theory -- Moduli theory and weighted spaces -- Gluing instantons -- Gluing in the reducible case -- Appendix A: further analytical results -- Convergence in the general case -- Gluing in the Morse--Bott case -- The Floer homology groups -- Compactness properties -- Floer's instanton homology groups -- Independence of metric -- Orientations -- Deforming the equations -- Transversality arguments -- U(2) and SO(3) connections -- Floer homology and 4-manifold invariants -- The conceptual picture -- The straightforward case -- Review of invariants for closed 4-manifolds -- Invariants for manifolds with boundary and b[superscript +]] 1 -- Reducible connections and cup products -- The maps D[subscript 1], D[subscript 2] -- Manifolds with b[superscript +] = 0, 1 -- The case b[superscript +] = 1. |
| Record Nr. | UNINA-9910809903203321 |
Donaldson S. K
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| Cambridge ; ; New York, : Cambridge University Press, 2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Riemann surfaces / / Simon Donaldson
| Riemann surfaces / / Simon Donaldson |
| Autore | Donaldson S. K |
| Pubbl/distr/stampa | Oxford ; ; New York : , : Oxford University Press, , 2011 |
| Descrizione fisica | 1 online resource (301 pages) : illustrations |
| Disciplina | 515.93 |
| Collana | Oxford graduate texts in mathematics |
| Soggetto topico |
Riemann surfaces
Functions |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-19-154584-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910453477903321 |
|
Donaldson S. K
|
||
| Oxford ; ; New York : , : Oxford University Press, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Riemann surfaces / / Simon Donaldson
| Riemann surfaces / / Simon Donaldson |
| Autore | Donaldson S. K |
| Pubbl/distr/stampa | Oxford ; ; New York : , : Oxford University Press, , 2011 |
| Descrizione fisica | 1 online resource (301 pages) : illustrations |
| Disciplina | 515.93 |
| Collana | Oxford graduate texts in mathematics |
| Soggetto topico |
Riemann surfaces
Functions |
| ISBN | 0-19-154584-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910790525003321 |
|
Donaldson S. K
|
||
| Oxford ; ; New York : , : Oxford University Press, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Riemann surfaces / / Simon Donaldson
| Riemann surfaces / / Simon Donaldson |
| Autore | Donaldson S. K |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Oxford ; ; New York : , : Oxford University Press, , 2011 |
| Descrizione fisica | 1 online resource (301 pages) : illustrations |
| Disciplina | 515.93 |
| Collana | Oxford graduate texts in mathematics |
| Soggetto topico |
Riemann surfaces
Functions |
| ISBN | 0-19-154584-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Contents -- PART I: PRELIMINARIES -- 1 Holomorphic functions -- 1.1 Simple examples: algebraic functions -- 1.2 Analytic continuation: differential equations -- Exercises -- 2 Surface topology -- 2.1 Classification of surfaces -- 2.2 Discussion: the mapping class group -- Exercises -- PART II: BASIC THEORY -- 3 Basic definitions -- 3.1 Riemann surfaces and holomorphic maps -- 3.2 Examples -- Exercises -- 4 Maps between Riemann surfaces -- 4.1 General properties -- 4.2 Monodromy and the Riemann Existence Theorem -- Exercises -- 5 Calculus on surfaces -- 5.1 Smooth surfaces -- 5.2 de Rham cohomology -- 5.3 Calculus on Riemann surfaces -- Exercises -- 6 Elliptic functions and integrals -- 6.1 Elliptic integrals -- 6.2 The Weierstrass [Omitted] function -- 6.3 Further topics -- Exercises -- 7 Applications of the Euler characteristic -- 7.1 The Euler characteristic and meromorphic forms -- 7.2 Applications -- Exercises -- PART III: DEEPER THEORY -- 8 Meromorphic functions and the Main Theorem for compact Riemann surfaces -- 8.1 Consequences of the Main Theorem -- 8.2 The Riemann-Roch formula -- Exercises -- 9 Proof of the Main Theorem -- 9.1 Discussion and motivation -- 9.2 The Riesz Representation Theorem -- 9.3 The heart of the proof -- 9.4 Weyl's Lemma -- Exercises -- 10 The Uniformisation Theorem -- 10.1 Statement -- 10.2 Proof of the analogue of the Main Theorem -- Exercises -- PART IV: FURTHER DEVELOPMENTS -- 11 Contrasts in Riemann surface theory -- 11.1 Algebraic aspects -- 11.2 Hyperbolic surfaces -- Exercises -- 12 Divisors, line bundles and Jacobians -- 12.1 Cohomology and line bundles -- 12.2 Jacobians of Riemann surfaces -- Exercises -- 13 Moduli and deformations -- 13.1 Almost-complex structures, Beltrami differentials and the integrability theorem -- 13.2 Deformations and cohomology -- 13.3 Appendix -- Exercises.
14 Mappings and moduli -- 14.1 Diffeomorphisms of the plane -- 14.2 Braids, Dehn twists and quadratic singularities -- 14.3 Hyperbolic geometry -- 14.4 Compactification of the moduli space -- Exercises -- 15 Ordinary differential equations -- 15.1 Conformal mapping -- 15.2 Periods of holomorphic forms and ordinary differential equations -- Exercises -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W. |
| Record Nr. | UNINA-9910811556803321 |
|
Donaldson S. K
|
||
| Oxford ; ; New York : , : Oxford University Press, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||