University of Michigan

**Time and location:** Tuesdays and Thursdays 2:30-4pm in East Hall 2866

**Instructor:** Linh Truong
(tlinh@umich.edu)

**Office hours:** By appointment

**Course Information: Syllabus **

Date | Topics | References |
---|---|---|

8/29 | Overview and motivating questions | |

8/31 | Heegaard diagrams for 3-manifolds |
[GS] p. 112-115
[OS-5] §2 |

9/5 | Morse theory | [Mil] p. 1-39 |

9/7 | Morse homology |
[McD] §1.1-1.2
[Hut] §2.1-2.4 [AD] §3, §4 |

9/12 | Lagrangian Floer homology |
[AD] §5, §6
[Aur] §1 |

9/14 | Lagrangian Floer homology | [Aur] §1 |

9/19 | Symmetric Products of Surfaces |
[OS-1] §2.1-2.4
[OS-5] §4, §5 |

9/21 | Heegaard Floer homology: definition | [OS-5] §7 |

9/26 | Maslov grading, admissible Heegaard diagrams, Turaev reformulation of spin^c structures | [OS-5] §6, §7 |

9/28 | Heegaard Floer homology: Invariance I | [OS-1] |

10/3 | Invariance II: Holomorphic triangles and rectangles | [OS-1] |

10/5 |
Heegaard Floer variants: minus, plus, infinity
Surgery Exact Triangle: statement and applications |
[OS-5] §8
[OS-6] §1 |

10/10 | Surgery Exact Triangle: Proof | [OS-6] §2 |

10/12 | Surgery on knots | [OS-6] §2 |

10/16 | fall break; no class | |

10/19 | Applications: L-spaces and Branched Double Covers | [OS-6] §1 |

10/24 | Cobordism maps | [OS-6] §3 |

10/26 | Absolute gradings, d-invariants, and computations | [OS-8] |

10/31 | Examples, nice diagrams and combinatorial HF |
[OS-7] §2.2
[SW] |

11/2 | Grid homology |
[Grid Homology]
[example] |

11/7 | Knot Floer homology: Definition | [Hom] |

11/9 |
Knot Floer homology: Examples
Definition of the tau invariant |
[Hom] |

11/14 | Heegaard Floer homology of knot surgery and computations | [Hom] |

- [Kho] A categorification of the Jones polynomial, Mikhail Khovanov.
- [Lee] An endomorphism of the Khovanov invariant, Eun Soo Lee.
- [OS-1] Holomorphic disks and topological invariants for closed three-manifolds, Peter Ozsváth and Zoltán Szabó.
- [OS-2] Holomorphic disks and three-manifold invariants: properties and applications, Peter Ozsváth and Zoltán Szabó.
- [OS-3] Holomorphic disks and knot invariants, Peter Ozsváth and Zoltán Szabó.
- [OS-4] Holomorphic triangles and invariants for smooth four-manifolds, Peter Ozsváth and Zoltán Szabó.
- [OS-8] Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Peter Ozsváth and Zoltán Szabó.
- [Ras] Floer homology and knot complements, Jacob Rasmussen.
- [R] Khovanov homology and the slice genus, Jacob Rasmussen.
- [SW] An algorithm to compute some Heegaard Floer homologies, Sucharit Sarkar and Jiajun Wang.

- [Aur] A beginner's introduction to Fukaya categories, Denis Auroux.
- [Gre] Heegaard Floer homology, Joshua Greene.
- [Hom] Lectures notes on Heegaard Floer homology, Jennifer Hom.
- [Hut] Lectures notes on Morse Homology, Michael Hutchings.
- [Lip] Heegaard Floer Homologies: lecture notes, Robert Lipshitz.
- [Man] An introduction to knot Floer homology, Ciprian Manolescu.
- [McD] Floer theory and low-dimensional topology, Dusa McDuff.
- [OS-5] An introduction to Heegaard Floer homology, Peter Ozsváth and Zoltán Szabó.
- [OS-6] Lectures on Heegaard Floer Homology, Peter Ozsváth and Zoltán Szabó.
- [OS-7] Heegaard diagrams and holomorphic disks, Peter Ozsváth and Zoltán Szabó.

- [AD] Morse theory and Floer homology, Michèle Audin and Mihai Damian.
- [GS] 4-Manifolds and Kirby Calculus, Robert Gompf and Andras Stipsicz.
- [Mil] Morse theory, John Milnor.