Time and location: Mondays, Wednesdays and Fridays, at 2:002:50pm, on Zoom
Instructor: Linh Truong (tlinh@umich.edu)
Office hours: Fridays after class, and by appointment, on Zoom
Course Information: Syllabus
Date  Topics  References 

1/20  Overview and goals  
1/22  Morse theory  [Mil] p. 139 
1/25  Morse homology 
[McD] §1.11.2
[Hut] §2.12.4 [AD] §3.13.2 
1/27  Morse homology: examples and applications  [AD] §3, §4 
1/29  Symplectic Manifolds, almost complex structures  [AD] §5 
2/1  Jholomorphic curves 
[AD] §6
[Aur] §1 
2/3  Lagrangian Floer homology  [Aur] §1 
2/5  Heegaard diagrams 
[GS] p. 112115
[OS5] §2 
2/8  Heegaard moves  [OS5] §2 
2/10  Symmetric product of surfaces  [OS1] §2.12.4 
2/12  Disks in symmetric product, totally real tori  [OS5] §4, §5 
2/15  Heegaard Floer homology: definition  [OS5] §7 
2/17  Maslov grading, admissible Heegaard diagrams  [OS5] §7 
2/19  Turaev reformulation of spin^c structures  [OS5] §6 
2/22  Heegaard Floer homology: Invariance I  [OS1] 
2/24  university wellbeing break (no class)  
2/26  Invariance II: Holomorphic triangles and rectangles  [OS1] 
3/1 
Heegaard Floer variants: minus, plus, infinity
Surgery Exact Triangle: statement and applications 
[OS5] §8
[OS6] §1 
3/3  Surgery Exact Triangle: Proof I  [OS6] §2 
3/5  Surgery Exact Triangle: Proof II  [OS6] §2 
3/8  Applications: Lspaces and Branched Double Covers  [OS6] §1 
3/10  Cobordism maps  [OS6] §3 
3/12  Absolute gradings, dinvariants, and computations  [OS8] 
3/15  Examples, nice diagrams and combinatorial HF 
[OS7] §2.2
[SW] 
3/17  Khovanov homology 
[Kho]

3/19  Lee homology  [Lee] 
3/22  no class  
3/24  no class  
3/26  student presentation (Rasmussen sinvariant)  [R] 
3/29  Proof of Rasmussen's slice genus bound, part I  [R] 
3/31  Proof of Rasmussen's slice genus bound, part II  [R] 
4/2  HF of branched double covers  [OScovers] 
4/5  Closed 4manifold invariant  [OS4] 
4/7  student presentation: Lspaces and taut foliations  [OSgenus] 
4/9  Knot Floer homology: Definition  [Hom] 
4/12 
Knot Floer homology: Examples
Definition of the tau invariant 
[Hom] 
4/14  Heegaard Floer homology of knot surgery and computations  [Hom] 
4/16  student presentation: A Khovanov Homotopy Type  [LS] 
4/19  Grid homology 
[Grid Homology]
[example] 
4/21  Knot concordance group homomorphisms  [DHST] 