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The decomposition of global conformal invariants /
This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. Thes...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2012.
|
| Colección: | Annals of mathematics studies ;
no. 182. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Alexakis, Spyros, |d 1978- | |
| 245 | 1 | 4 | |a The decomposition of global conformal invariants / |c Spyros Alexakis. |
| 260 | |a Princeton : |b Princeton University Press, |c 2012. | ||
| 300 | |a 1 online resource (460 pages) | ||
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| 490 | 1 | |a Annals of mathematics studies ; |v no. 182 | |
| 505 | 0 | |6 880-01 |a Cover Page; Title Page; Copyright Page; Table of Contents; Acknowledgments; 1. Introduction; 1.1 Related Questions; 1.2 Outline of this Work; 2. An Iterative Decomposition of Global Conformal Invariants: The First Step; 2.1 Introduction; 2.2 Conventions, Background, and the Super Divergence Formula; 2.3 From the super Divergence Formula for Ig(ø) Back to P(g): The Two Main Claims of this Work; 2.4 Proposition 2.7 in the Easy Case s = s; 2.5 Proposition 2.7 in the Hard Case s <s; 3. The Second Step: The Fefferman-Graham Ambient Metric and the Nature of the Decomposition; 3.1 Introduction. | |
| 505 | 8 | |a 3.2 The Locally Conformally Invariant Piece in P(g): A Proof of Lemmas 3.1, 3.2, and 3.33.3 Proof of Lemma 3.4: The Divergence Piece in P(g); 4. A Result on the Structure of Local Riemannian Invariants: The Fundamental Proposition; 4.1 Introduction; 4.2 The fundamental Proposition 4.13; 4.3 Proof of Proposition 4.13: Set up an Induction and Reduce the Inductive Step to Lemmas 4.16, 4.19, 4.24; 4.4 Proof that Proposition 4.13 Follows from Lemmas 4.16, 4.19, and 4.24 (and Lemmas 4.22 and 4.23); 5. The Inductive Step of the Fundamental Proposition: The Simpler Cases; 5.1 Introduction. | |
| 505 | 8 | |a 5.2 Notation and Preliminary Results5.3 An analysis of Curvtrans[Lg]; 5.4 A study of LC[Lg] and W[Lg] in (5.16): Computations and cancellations; 6. The Inductive Step of the Fundamental Proposition: The Hard Cases, Part I; 6.1 Introduction; 6.2 The First Ingredient in the Grand Conclusion; 6.3 The Second Part of the Grand Conclusion: A study of Image 1,ß Øu+1 [Lg]=0; 6.4 The Grand Conclusion and the Proof of Lemma 4.24; 7. The Inductive Step of the Fundamental Proposition: The Hard Cases, Part II; 7.1 Introduction: A sketch of the Strategy; 7.2 The proof of Lemma 4.24 in Case B; A. Appendix. | |
| 505 | 8 | |a A.1 Some Technical ToolsA. 2 Some Postponed Short Proofs; A.3 Proof of Lemmas 4.22 and 4.23; Bibliography; Index of Authors and Terms; Index of Symbols. | |
| 520 | |a This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 546 | |a In English. | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 650 | 0 | |a Conformal invariants. | |
| 650 | 0 | |a Decomposition (Mathematics) | |
| 650 | 6 | |a Invariants conformes. | |
| 650 | 6 | |a Décomposition (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Numerical Analysis. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Differential. |2 bisacsh | |
| 650 | 7 | |a Conformal invariants. |2 fast |0 (OCoLC)fst00875030 | |
| 650 | 7 | |a Decomposition (Mathematics) |2 fast |0 (OCoLC)fst00889127 | |
| 776 | 0 | 8 | |i Print version: |a Alexakis, Spyros. |t Decomposition of Global Conformal Invariants (AM-182). |d Princeton : Princeton University Press, 2012 |z 9780691153476 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 182. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt7rqqs |z Texto completo |
| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g 1. |t Introduction -- |g 1.1. |t Related questions -- |g 1.2. |t Outline of this work -- |g 2. |t Iterative Decomposition of Global Conformal Invariants: The First Step -- |g 2.1. |t Introduction -- |g 2.2. |t Conventions, background, and the super divergence formula -- |g 2.3. |t From the super divergence formula for Ig (ø) back to P(g): The two main claims of this work -- |g 2.4. |t Proposition 2.7 in the easy case s = σ -- |g 2.5. |t Proposition 2.7 in the hard case s <σ -- |g 3. |t Second Step: The Fefferman-Graham Ambient Metric and the Nature of the Decomposition -- |g 3.1. |t Introduction -- |g 3.2. |t locally conformally invariant piece in P(g): A proof of Lemmas 3.1, 3.2, and 3.3 -- |g 3.3. |t Proof of Lemma 3.4: The divergence piece in P(g) -- |g 4. |t Result on the Structure of Local Riemannian Invariants: The Fundamental Proposition -- |g 4.1. |t Introduction -- |g 4.2. |t fundamental Proposition 4.13 -- |g 4.3. |t Proof of Proposition 4.13: Set up an induction and reduce the inductive step to Lemmas 4.16, 4.19, 4.24 -- |g 4.4. |t Proof that Proposition 4.13 follows from Lemmas 4.16, 4.19, and 4.24 (and Lemmas 4.22 and 4.23) -- |g 5. |t Inductive Step of the Fundamental Proposition: The Simpler Cases -- |g 5.1. |t Introduction -- |g 5.2. |t Notation and preliminary results -- |g 5.3. |t analysis of CurvTrans[Lg] -- |g 5.4. |t study of LC[Lg] and W[Lg] in (5.16): Computations and cancellations -- |g 6. |t Inductive Step of the Fundamental Proposition: The Hard Cases, Part I -- |g 6.1. |t Introduction -- |g 6.2. |t first ingredient in the grand conclusion -- |g 6.3. |t second part of the grand conclusion: A study of Image 1, β ø u + 1[Lg] =0 -- |g 6.4. |t grand conclusion and the proof of Lemma 4.24 -- |g 7. |t Inductive Step of the Fundamental Proposition: The Hard Cases, Part II -- |g 7.1. |t Introduction: A sketch of the strategy -- |g 7.2. |t proof of Lemma 4.24 in Case B -- |g A. |t Appendix -- |g A.1. |t Some technical tools -- |g A.2. |t Some postponed short proofs -- |g A.3. |t Proof of Lemmas 4.22 and 4.23. |
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