Math285Z: Sutured 3-manifolds and Floer homology

 Time: 3:00-4:15 pm, Monday-Wednesday

Place: Science Center 105

Instructor: Fan Ye, Science Center 505H, fanye@math.harvard.edu

Course Assistant: Jiakai Li, SC 321G

Office Hours: 

Fan Ye, SC 505H, Monday, 4:20-5:20pm; Wednesday, 2:00-3:00 pm.

CA, SC321G, Thursday, 6:00-7:00pm.

Prerequisites:

• Differential geometry, especially principal bundle. Ref: a) Differential Geometry: Bundles, Connections, Metrics and Curvature, Chapters 1-16, Clifford H. Taubes; b) An Introduction to Differentiable Manifolds and Riemannian Geometry, William M. Boothby; c) Fundations of differentiable manifolds and Lie groups, Frank W. Warner.
• Algebraic topology, especially homology theory, characteristic classes, and spectral sequences. Ref: a) Algebraic Topology; b) Vector Bundles and K-Theory; both by Allen Hatcher; c) Differential forms in algebraic geometry, Chapters 4-5, Raoul Bott and Loring W. Tu.
• 3-manifold topology. Ref: Notes on Basic 3-Manifold Topology, Allen Hatcher.

Tentative Course Outline: Most references are papers. Notes will be posted on the course page after the classes. The names in the references denote the corresponding documents

• Weeks 1-2 (Jan. 22-31): Introduction to sutured manifolds. Ref: Lipshitz, Juhász
• Weeks 3-4 (Feb. 5-14): Sutured Heegaard Floer homology. Ref: Lipshitz, Juhász, Manolescu
• Weeks 5-6 (Feb. 19-28, with a holiday on Feb. 19): Sutured monopole Floer homology. Ref: Lin, Kronheimer-Mrowka
• Weeks 7-9 (Mar. 4-20, with spring break during Mar. 9-17): Sutured instanton Floer homology. Ref: Wang, Kronheimer-Mrowka
• Weeks 10-11 (Mar. 25-Apr. 3): Contact elements and surgery exact triangles. Ref: Sahamie, Oszváth-Szabó
• Weeks 12-14 (Apr. 8-24): Towards isomorphism of Floer homology. Ref: TBD