Floer Cohomology and Flips.

Format:

Book

Author/Creator:

Charest, François.

Contributor:

Woodward, Chris T.

Series:

Memoirs of the American Mathematical Society

Memoirs of the American Mathematical Society ; v.279

Language:

English

Subjects (All):

Floer homology.

Physical Description:

1 online resource (178 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2022.

Summary:

"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"-- Provided by publisher.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Charest, François Floer Cohomology and Flips

ISBN:

9781470472269

1470472260

OCLC:

1343247640