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Circle-valued Morse theory [[electronic resource] /] / Andrei V. Pajitnov
| Circle-valued Morse theory [[electronic resource] /] / Andrei V. Pajitnov |
| Autore | Pajitnov Andrei V |
| Pubbl/distr/stampa | Berlin ; ; New York, : De Gruyter, c2006 |
| Descrizione fisica | 1 online resource (464 pages) |
| Disciplina | 514/.74 |
| Collana | De Gruyter studies in mathematics |
| Soggetto topico |
Morse theory
Manifolds (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-19426-7
9786612194269 3-11-019797-9 |
| Classificazione | SK 350 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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 |
| Record Nr. | UNINA-9910454619003321 |
Pajitnov Andrei V
|
||
| Berlin ; ; New York, : De Gruyter, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Circle-valued Morse theory [[electronic resource] /] / Andrei V. Pajitnov
| Circle-valued Morse theory [[electronic resource] /] / Andrei V. Pajitnov |
| Autore | Pajitnov Andrei V |
| Pubbl/distr/stampa | Berlin ; ; New York, : De Gruyter, c2006 |
| Descrizione fisica | 1 online resource (464 pages) |
| Disciplina | 514/.74 |
| Collana | De Gruyter studies in mathematics |
| Soggetto topico |
Morse theory
Manifolds (Mathematics) |
| Soggetto non controllato |
Differential geometry
Morse theory |
| ISBN |
1-282-19426-7
9786612194269 3-11-019797-9 |
| Classificazione | SK 350 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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 |
| Record Nr. | UNINA-9910782523503321 |
|
Pajitnov Andrei V
|
||
| Berlin ; ; New York, : De Gruyter, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Circle-valued Morse theory / / Andrei V. Pajitnov
| Circle-valued Morse theory / / Andrei V. Pajitnov |
| Autore | Pajitnov Andrei V |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Berlin ; ; New York, : De Gruyter, c2006 |
| Descrizione fisica | 1 online resource (464 pages) |
| Disciplina | 514/.74 |
| Collana | De Gruyter studies in mathematics |
| Soggetto topico |
Morse theory
Manifolds (Mathematics) |
| Soggetto non controllato |
Differential geometry
Morse theory |
| ISBN |
1-282-19426-7
9786612194269 3-11-019797-9 |
| Classificazione | SK 350 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 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 |
| Record Nr. | UNINA-9910825910603321 |
|
Pajitnov Andrei V
|
||
| Berlin ; ; New York, : De Gruyter, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Infinite dimensional Morse theory and multiple solution problems / Kung-Ching Chang
| Infinite dimensional Morse theory and multiple solution problems / Kung-Ching Chang |
| Autore | Chang, Kung-Ching |
| Pubbl/distr/stampa | Boston : Birkhäuser, 1993 |
| Descrizione fisica | x, 312 p. ; 24 cm |
| Disciplina | 515 |
| Collana | Progress in nonlinear differential equations and their applications ; 6 |
| Soggetto topico | Morse theory |
| ISBN | 0817634517 |
| Classificazione | AMS 57R70 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000995269707536 |
|
Chang, Kung-Ching
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| Boston : Birkhäuser, 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
An invitation to Morse theory / Liviu I. Nicolaescu
| An invitation to Morse theory / Liviu I. Nicolaescu |
| Autore | Nicolaescu, Liviu I. |
| Pubbl/distr/stampa | New York ; London : Springer, 2007 |
| Descrizione fisica | xiv, 241 p. : 24 cm |
| Disciplina | 514.74 |
| Collana | Universitext |
| Soggetto topico | Morse theory |
| ISBN |
9780387495095
0387495096 038749510X 9780387495101 |
| Classificazione |
AMS 57R70
LC QA331.N498 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991003588029707536 |
|
Nicolaescu, Liviu I.
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| New York ; London : Springer, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Lectures on morse homology / Augustin Banyaga and David Hurtubise
| Lectures on morse homology / Augustin Banyaga and David Hurtubise |
| Autore | Banyaga, Augustin |
| Pubbl/distr/stampa | Dordrecht ; Boston ; London : Kluwer Academic Publishers, c2004 |
| Descrizione fisica | vii, 324 p. : ill. ; 25 cm |
| Disciplina | 515.73 |
| Altri autori (Persone) | Hurtubise, Davidauthor |
| Collana | Kluwer texts in the mathematical sciences ; 29 |
| Soggetto topico |
Morse theory
Homology theory |
| ISBN | 1402026951 |
| Classificazione | AMS 58E05 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000915479707536 |
|
Banyaga, Augustin
|
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| Dordrecht ; Boston ; London : Kluwer Academic Publishers, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Metrics of positive scalar curvature and generalised Morse functions Part I / / Mark Walsh
| Metrics of positive scalar curvature and generalised Morse functions Part I / / Mark Walsh |
| Autore | Walsh Mark |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (80 p.) |
| Disciplina | 516.3/62 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Curvature
Morse theory Riemannian manifolds Algebraic topology |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0597-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""0.1. Background""; ""0.2. Main results""; ""0.3. The connection with generalised Morse functions and Part II""; ""0.4. Acknowledgements""; ""Chapter 1. Definitions and Preliminary Results""; ""1.1. Isotopy and concordance in the space of metrics of positive scalar curvature""; ""1.2. Warped product metrics on the sphere""; ""1.3. Torpedo metrics on the disk""; ""1.4. Doubly warped products and mixed torpedo metrics""; ""1.5. Inducing a mixed torpedo metric with an embedding""; ""Chapter 2. Revisiting the Surgery Theorem""
""2.1. Surgery and cobordism""""2.2. Surgery and positive scalar curvature""; ""2.3. Outline of the proof of Theorem 2.3""; ""2.4. Part 1 of the proof: Curvature formulae for the first deformation""; ""2.5. Part 2 of the proof: A continuous bending argument""; ""2.6. Part 3 of the proof: Isotoping to a standard product""; ""2.7. Applying Theorem 2.3 over a compact family of psc-metrics""; ""2.8. The proof of Theorem 2.2 (The Improved Surgery Theorem)""; ""Chapter 3. Constructing Gromov-Lawson Cobordisms""; ""3.1. Morse Theory and admissible Morse functions"" ""3.2. A reverse Gromov-Lawson cobordism""""3.3. Continuous families of Morse functions""; ""Chapter 4. Constructing Gromov-Lawson Concordances""; ""4.1. Applying the Gromov-Lawson technique over a pair of cancelling surgeries""; ""4.2. Cancelling Morse critical points: The Weak and Strong Cancellation Theorems""; ""4.3. A strengthening of Theorem 4.2""; ""4.4. Standardising the embedding of the second surgery sphere""; ""Chapter 5. Gromov-Lawson Concordance Implies Isotopy for Cancelling Surgeries""; ""5.1. Connected sums of psc-metrics"" ""5.2. An analysis of the metric g'', obtained from the second surgery""""5.3. The proof of Theorem 5.1""; ""Chapter 6. Gromov-Lawson Concordance Implies Isotopy in the General Case""; ""6.1. A weaker version of Theorem 0.8""; ""6.2. The proof of the main theorem""; ""Appendix: Curvature Calculations from the Surgery Theorem""; ""Bibliography"" |
| Record Nr. | UNINA-9910480096203321 |
|
Walsh Mark
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Metrics of positive scalar curvature and generalised Morse functions Part I / / Mark Walsh
| Metrics of positive scalar curvature and generalised Morse functions Part I / / Mark Walsh |
| Autore | Walsh Mark |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (80 p.) |
| Disciplina | 516.3/62 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Curvature
Morse theory Riemannian manifolds Algebraic topology |
| ISBN | 1-4704-0597-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""0.1. Background""; ""0.2. Main results""; ""0.3. The connection with generalised Morse functions and Part II""; ""0.4. Acknowledgements""; ""Chapter 1. Definitions and Preliminary Results""; ""1.1. Isotopy and concordance in the space of metrics of positive scalar curvature""; ""1.2. Warped product metrics on the sphere""; ""1.3. Torpedo metrics on the disk""; ""1.4. Doubly warped products and mixed torpedo metrics""; ""1.5. Inducing a mixed torpedo metric with an embedding""; ""Chapter 2. Revisiting the Surgery Theorem""
""2.1. Surgery and cobordism""""2.2. Surgery and positive scalar curvature""; ""2.3. Outline of the proof of Theorem 2.3""; ""2.4. Part 1 of the proof: Curvature formulae for the first deformation""; ""2.5. Part 2 of the proof: A continuous bending argument""; ""2.6. Part 3 of the proof: Isotoping to a standard product""; ""2.7. Applying Theorem 2.3 over a compact family of psc-metrics""; ""2.8. The proof of Theorem 2.2 (The Improved Surgery Theorem)""; ""Chapter 3. Constructing Gromov-Lawson Cobordisms""; ""3.1. Morse Theory and admissible Morse functions"" ""3.2. A reverse Gromov-Lawson cobordism""""3.3. Continuous families of Morse functions""; ""Chapter 4. Constructing Gromov-Lawson Concordances""; ""4.1. Applying the Gromov-Lawson technique over a pair of cancelling surgeries""; ""4.2. Cancelling Morse critical points: The Weak and Strong Cancellation Theorems""; ""4.3. A strengthening of Theorem 4.2""; ""4.4. Standardising the embedding of the second surgery sphere""; ""Chapter 5. Gromov-Lawson Concordance Implies Isotopy for Cancelling Surgeries""; ""5.1. Connected sums of psc-metrics"" ""5.2. An analysis of the metric g'', obtained from the second surgery""""5.3. The proof of Theorem 5.1""; ""Chapter 6. Gromov-Lawson Concordance Implies Isotopy in the General Case""; ""6.1. A weaker version of Theorem 0.8""; ""6.2. The proof of the main theorem""; ""Appendix: Curvature Calculations from the Surgery Theorem""; ""Bibliography"" |
| Record Nr. | UNINA-9910788859803321 |
|
Walsh Mark
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Metrics of positive scalar curvature and generalised Morse functions Part I / / Mark Walsh
| Metrics of positive scalar curvature and generalised Morse functions Part I / / Mark Walsh |
| Autore | Walsh Mark |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (80 p.) |
| Disciplina | 516.3/62 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Curvature
Morse theory Riemannian manifolds Algebraic topology |
| ISBN | 1-4704-0597-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Introduction""; ""0.1. Background""; ""0.2. Main results""; ""0.3. The connection with generalised Morse functions and Part II""; ""0.4. Acknowledgements""; ""Chapter 1. Definitions and Preliminary Results""; ""1.1. Isotopy and concordance in the space of metrics of positive scalar curvature""; ""1.2. Warped product metrics on the sphere""; ""1.3. Torpedo metrics on the disk""; ""1.4. Doubly warped products and mixed torpedo metrics""; ""1.5. Inducing a mixed torpedo metric with an embedding""; ""Chapter 2. Revisiting the Surgery Theorem""
""2.1. Surgery and cobordism""""2.2. Surgery and positive scalar curvature""; ""2.3. Outline of the proof of Theorem 2.3""; ""2.4. Part 1 of the proof: Curvature formulae for the first deformation""; ""2.5. Part 2 of the proof: A continuous bending argument""; ""2.6. Part 3 of the proof: Isotoping to a standard product""; ""2.7. Applying Theorem 2.3 over a compact family of psc-metrics""; ""2.8. The proof of Theorem 2.2 (The Improved Surgery Theorem)""; ""Chapter 3. Constructing Gromov-Lawson Cobordisms""; ""3.1. Morse Theory and admissible Morse functions"" ""3.2. A reverse Gromov-Lawson cobordism""""3.3. Continuous families of Morse functions""; ""Chapter 4. Constructing Gromov-Lawson Concordances""; ""4.1. Applying the Gromov-Lawson technique over a pair of cancelling surgeries""; ""4.2. Cancelling Morse critical points: The Weak and Strong Cancellation Theorems""; ""4.3. A strengthening of Theorem 4.2""; ""4.4. Standardising the embedding of the second surgery sphere""; ""Chapter 5. Gromov-Lawson Concordance Implies Isotopy for Cancelling Surgeries""; ""5.1. Connected sums of psc-metrics"" ""5.2. An analysis of the metric g'', obtained from the second surgery""""5.3. The proof of Theorem 5.1""; ""Chapter 6. Gromov-Lawson Concordance Implies Isotopy in the General Case""; ""6.1. A weaker version of Theorem 0.8""; ""6.2. The proof of the main theorem""; ""Appendix: Curvature Calculations from the Surgery Theorem""; ""Bibliography"" |
| Record Nr. | UNINA-9910827647903321 |
|
Walsh Mark
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Minimal resolutions via algebraic discrete morse theory / / Michael J©œllenbeck, Volkmar Welker
| Minimal resolutions via algebraic discrete morse theory / / Michael J©œllenbeck, Volkmar Welker |
| Autore | J©œllenbeck Michael <1975-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (88 p.) |
| Disciplina | 514 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Morse theory
Free resolutions (Algebra) Algebra |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0529-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""1. Hochschild Homology and Discrete Morse Theory""""2. Explicit Calculations of Hochschild Homology""; ""Chapter 6. Minimal (Cellular) Resolutions for (p-)Borel Fixed Ideals""; ""1. Cellular Resolutions""; ""2. Cellular Minimal Resolution for Principal Borel Fixed Ideals""; ""3. Cellular Minimal Resolution for a Class of p-Borel Fixed Ideals""; ""Appendix A. The Bar and the Hochschild Complex""; ""Appendix B. Proofs for Algebraic Discrete Morse Theory""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""; ""P""; ""R""
""S""""T""; ""V""; ""W"" |
| Record Nr. | UNINA-9910480858303321 |
|
J©œllenbeck Michael <1975->
|
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| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Morse theory
(20)
- Algebra (3)
- Algebraic topology (3)
- Curvature (3)
- Floer homology (3)