|
Heegaard Floer Homology Seminar Wednesdays at 4:30 |
The goal of this seminar is to read through one
or two papers by Peter Oszvath and Zoltan Szabo:
SG/0101206
and
SG/0105202.
The first couple of weeks, however, we will cover some foundational material.
| February 9 | Mike Sullivan, "Morse Homology" |
We discuss how to recover the homology of a manifold from a the gradient flows of a Morse function. This construction serves as a finite-dimensional model for Floer homology, with the "moduli space" of gradient flows playing the role of the moduli space of holomorphic curves. |
| February 16 | Hao Wu, "Heegaard diagrams and symmetric products of surfaces" |
This will be the first of many lectures discussing Heegard Floer homology. Specifically, it will focus on Section 2 of SG/0101206. |
| February 23 | Mike Sullivan, "Morse Theory and Lagrangian Floer homology" |
We finish the dicsussion of Morse theory from 2/9. We define symplectic and Lagrangian manifolds, as well as almost complex structures and holomorphic curves. We present Floer's original construction of Lagrangian Floer homology, the ancestor of Heegaard Floer homology. |
| March 2 | Mike Sullivan, "Lagrangian Floer homology II". |
See previous talk description. |
| March 9 | Mike Sullivan, "Moduli spaces and orientations" |
Section 3 |
| March 16 | Spring Break |
|
| March 23 | postponed due to faculty meeting |
|
| March 30 | Hao Wu, "Heegaard Floer homology--definition" |
We discuss the definition and some basic properties of the Heegaard Floer homology. (Sections 4 and 5) |
| April 6 | Hao Wu, "Adjunction Inequalities" |
Section 7 of SG/0105202 |
| April 13 | Hao Wu, "Adjunction II" |
|
| April 20 | No meeting |
|
| April 27 | Mike Sullivan, "Invariance" |
Sections 6 and 7. |
| May 4 | Hao Wu, "Holomrphic triangles I" |
Section 8 |
| May 11 | ??, "??" |
?? |