# Math285Z: Sutured 3-manifolds and Floer homology Semester: Spring | Year offered: 2024 Time: 3:00-4:15 pm, Monday-Wednesday Place: Science Center 105 Instructor: Fan Ye, Science Center 505H, 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 --- Attachments- [ picture\_as\_pdf syllabus\_math285z.pdf ](/sites/g/files/omnuum10216/files/fanye/files/syllabus_math285z.pdf) - [ picture\_as\_pdf juhasz\_a\_surgery\_of\_heegaard\_floer\_homology.pdf ](/sites/g/files/omnuum10216/files/fanye/files/juhasz_a_surgery_of_heegaard_floer_homology.pdf) - [ picture\_as\_pdf lipshitz\_heegaard\_floer\_homology.pdf ](/sites/g/files/omnuum10216/files/fanye/files/lipshitz_heegaard_floer_homology.pdf) - [ picture\_as\_pdf lin\_lectures\_on\_monopole\_floer\_homology.pdf ](/sites/g/files/omnuum10216/files/fanye/files/lin_lectures_on_monopole_floer_homology.pdf) - [ picture\_as\_pdf ozsvath-szabo\_lectures\_on\_heegaard\_floer\_homology.pdf ](/sites/g/files/omnuum10216/files/fanye/files/ozsvath-szabo_lectures_on_heegaard_floer_homology.pdf) - [ picture\_as\_pdf wang\_18.937\_lecture\_notes.pdf ](/sites/g/files/omnuum10216/files/fanye/files/wang_18.937_lecture_notes.pdf) - [ picture\_as\_pdf manolescu\_an\_introduction\_to\_knot\_floer\_homology.pdf ](/sites/g/files/omnuum10216/files/fanye/files/manolescu_an_introduction_to_knot_floer_homology.pdf) - [ picture\_as\_pdf sahamie\_heegaard\_contact\_elements.pdf ](/sites/g/files/omnuum10216/files/fanye/files/sahamie_heegaard_contact_elements.pdf) - [ picture\_as\_pdf ozsvath-szabo\_an\_introduction\_to\_heegaard\_floer\_homology.pdf ](/sites/g/files/omnuum10216/files/fanye/files/ozsvath-szabo_an_introduction_to_heegaard_floer_homology.pdf) - [ picture\_as\_pdf lecture\_1.pdf ](/sites/g/files/omnuum10216/files/fanye/files/lecture_1.pdf) - [ picture\_as\_pdf 285z\_pset1.pdf ](/sites/g/files/omnuum10216/files/fanye/files/285z_pset1.pdf) - [ picture\_as\_pdf math285z\_week\_1-2\_suture.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math285z_week_1-2_suture.pdf) - [ picture\_as\_pdf 285z\_pset2.pdf ](/sites/g/files/omnuum10216/files/fanye/files/285z_pset2.pdf) - [ picture\_as\_pdf math285z\_week\_3-4\_heegaard.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math285z_week_3-4_heegaard.pdf) - [ picture\_as\_pdf pset3.pdf ](/sites/g/files/omnuum10216/files/fanye/files/pset3.pdf) - [ picture\_as\_pdf math285z\_week\_5-6\_monopole\_updated.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math285z_week_5-6_monopole_updated.pdf) - [ picture\_as\_pdf 285z\_pset4.pdf ](/sites/g/files/omnuum10216/files/fanye/files/285z_pset4.pdf) - [ picture\_as\_pdf pset5.pdf ](/sites/g/files/omnuum10216/files/fanye/files/pset5.pdf) - [ picture\_as\_pdf 285z\_pset6.pdf ](/sites/g/files/omnuum10216/files/fanye/files/285z_pset6.pdf) - [ picture\_as\_pdf math285z\_week\_7-9\_instanton\_updated.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math285z_week_7-9_instanton_2.pdf) - [ picture\_as\_pdf math285z\_week\_10-11\_triangle\_updated.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math285z_week_10-11_triangle_2.pdf) - [ picture\_as\_pdf floer\_class\_final.pdf ](/sites/g/files/omnuum10216/files/fanye/files/floer_class_final.pdf) ---