Floer Cohomology and Flips

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Charest and Woodward 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 singularly-free running of the minimal model program, they say, which is analogous to the description of Bondal-Orlav (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. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)

Author(s): Francois Charest, Chris T. Woodward
Series: Memoirs of the American Mathematical Society, 1372
Publisher: American Mathematical Society
Year: 2022

Language: English
Pages: 177
City: Providence

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