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Record Nr. |
UNINA9910825910603321 |
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Autore |
Pajitnov Andrei V |
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Titolo |
Circle-valued Morse theory [[electronic resource] /] / Andrei V. Pajitnov |
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Pubbl/distr/stampa |
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Berlin ; ; New York, : De Gruyter, c2006 |
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ISBN |
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1-282-19426-7 |
9786612194269 |
3-11-019797-9 |
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Descrizione fisica |
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1 online resource (464 pages) |
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Collana |
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De Gruyter studies in mathematics, , 0179-0986 ; ; 32 |
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Classificazione |
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Disciplina |
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Soggetti |
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Morse theory |
Manifolds (Mathematics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. [437]-444) and index. |
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Nota di contenuto |
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Front matter -- Contents -- Preface -- Introduction -- Part 1. Morse functions and vector fields on manifolds -- CHAPTER 1. Vector fields and C0 topology -- CHAPTER 2. Morse functions and their gradients -- CHAPTER 3. Gradient flows of real-valued Morse functions -- Part 2. Transversality, handles, Morse complexes -- CHAPTER 4. The Kupka-Smale transversality theory for gradient flows -- CHAPTER 5. Handles -- CHAPTER 6. The Morse complex of a Morse function -- Part 3. Cellular gradients -- CHAPTER 7. Condition (C) -- CHAPTER 8. Cellular gradients are C0-generic -- CHAPTER 9. Properties of cellular gradients -- Part 4. Circle-valued Morse maps and Novikov complexes -- CHAPTER 10. Completions of rings, modules and complexes -- CHAPTER 11. The Novikov complex of a circle-valued Morse map -- CHAPTER 12. Cellular gradients of circle-valued Morse functions and the Rationality Theorem -- CHAPTER 13. Counting closed orbits of the gradient flow -- CHAPTER 14. Selected topics in the Morse-Novikov theory -- Backmatter |
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Sommario/riassunto |
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In the early 1920's M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. Circle-valued Morse theory originated from a problem in |
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