Metrics of positive scalar curvature and generalised Morse functions Part I / / Mark Walsh

• Record Nr.: UNINA9910480096203321
• Autore: Walsh Mark
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2010; ©2010
• ISBN: 1-4704-0597-0
• Descrizione fisica: 1 online resource (80 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Number 983
• Disciplina: 516.3/62
• Soggetti: Curvature; Morse theory; Riemannian manifolds; Algebraic topology; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 209, number 983 (second of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• 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""