Author(s): Paul Biran, Octav Cornea, Egor Shelukhin
Series: Astérisque 426
Publisher: Société Mathématique de France
Year: 2021
Language: English
Pages: 128
Chapter 1. Introduction and main results
1.1. Decomposition by Lagrangian cobordism
1.2. Weighted fragmentation pseudo-metrics on triangulated categories
1.3. Outline of the proof of Theorem B
Acknowledgments
Chapter 2. Weakly filtered A-theory
2.1. Weakly filtered A-categories
2.2. Typical classes of examples
2.3. Weakly filtered A-functors and modules
2.4. Weakly filtered mapping cones
2.5. The -map
2.6. Structure theorem for weakly filtered iterated cones
2.7. Invariants and measurements for filtered chain complexes
Chapter 3. Floer theory and Fukaya categories
3.1. Units
3.2. Families of Fukaya categories
3.3. Weakly filtered structure on Fukaya categories
3.4. Extending the theory to Lagrangian cobordisms
3.5. The monotone case
3.6. Inclusion functors
3.7. Weakly filtered iterated cones coming from cobordisms
Chapter 4. Quasi-exact and quasi-monotone cobordisms
4.1. Quasi-exact cobordisms
4.2. Extending the results from Section 3.7 to quasi-exact cobordisms
4.3. Quasi-monotone cobordisms
4.4. Extending the results from Section 3.7 to quasi-monotone cobordisms
Chapter 5. Proof of the main geometric statements
5.1. Proof of Theorem 5.1
5.2. Proof of Theorem 5.2
5.3. The quasi-exact and quasi-monotone cases
Chapter 6. Metrics on spaces of Lagrangians and examples
6.1. Setting up the right class of cobordisms
6.2. Shadow metrics on spaces of Lagrangian submanifolds
6.3. Some examples and calculations
6.4. Algebraic metrics on L-1.5 mu a-1 mu g(M)
Bibliography
