Floer Cohomology and Flips

• Autore: Charest François
• Pubblicazione: Providence : , : American Mathematical Society, , 2022; ©2022
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (178 pages)
• Disciplina: 516.3/6; 516.36
• Soggetto topico: Floer homology; Differential geometry -- Symplectic geometry, contact geometry -- Floer homology and cohomology, symplectic aspects
• Classificazione: 53D40
• Altri autori: WoodwardChris T
• Nota di contenuto: Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Symplectic flips -- 2.1. Symplectic mmp runnings -- 2.2. Runnings for toric manifolds -- 2.3. Runnings for polygon spaces -- 2.4. Runnings for moduli spaces of flat bundles -- Chapter 3. Lagrangians associated to flips -- 3.1. Regular Lagrangians -- 3.2. Regular Lagrangians for toric manifolds -- 3.3. Regular Lagrangians for polygon spaces -- 3.4. Regular Lagrangians for moduli spaces of flat bundles -- Chapter 4. Fukaya algebras -- 4.1. \ainfty algebras -- 4.2. Associahedra -- 4.3. Treed pseudoholomorphic disks -- 4.4. Transversality -- 4.5. Compactness -- 4.6. Composition maps -- 4.7. Divisor equation -- 4.8. Maurer-Cartan moduli space -- Chapter 5. Homotopy invariance -- 5.1. \ainfty morphisms -- 5.2. Multiplihedra -- 5.3. Quilted pseudoholomorphic disks -- 5.4. Morphisms of Fukaya algebras -- 5.5. Homotopies -- 5.6. Stabilization -- Chapter 6. Fukaya bimodules -- 6.1. \ainfty bimodules -- 6.2. Treed strips -- 6.3. Hamiltonian perturbations -- 6.4. Clean intersections -- 6.5. Morphisms -- 6.6. Homotopies -- Chapter 7. Broken Fukaya algebras -- 7.1. Broken curves -- 7.2. Broken maps -- 7.3. Broken perturbations -- 7.4. Broken divisors -- 7.5. Reverse flips -- Chapter 8. The break-up process -- 8.1. Varying the length -- 8.2. Breaking a symplectic manifold -- 8.3. Breaking perturbation data -- 8.4. Getting back together -- 8.5. The infinite length limit -- 8.6. Examples -- Bibliography -- Back Cover.
• Sommario/riassunto: "We show that blow-ups or reverse flips (in the sense of the minimal model program) of rational symplectic manifolds with point centers create Floer-non-trivial Lagrangian tori. These results are part of a conjectural decomposition of the Fukaya category of a compact symplectic manifold with a singularity-free running of the minimal model program, analogous to the description of Bondal-Orlov (Derived categories of coherent sheaves, 2002) and Kawamata (Derived categories of toric varieties, 2006) of the bounded derived category of coherent sheaves on a compact complex manifold"--
• Titolo autorizzato: Floer Cohomology and Flips
• ISBN: 9781470472269; 1470472260
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910959959503321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society