All Questions
5 questions
12
votes
1
answer
986
views
Why is Heegaard Floer Homology defined in terms of Sym$^g\Sigma_g$ instead of Pic$^g\Sigma_g$?
Recall the definition of Heegaard Floer homology: $\Sigma_g$ is a closed surface, and $\{\alpha_1,\ldots,\alpha_g\}$ and $\{\beta_1,\ldots,\beta_g\}$ are sets of attaching circles. Then Heegaard ...
- 18.7k
6
votes
1
answer
602
views
Path of almost complex structure in the definition of Heegaard Floer homology
$\DeclareMathOperator\Sym{Sym}$In order to define Heegaard Floer Homology for a connected, closed, oriented 3 manifold, we fix a generic path of nearly symmetric almost complex structure $J_s$ over $\...
- 83
6
votes
0
answers
225
views
Is Heegaard-Floer homology the Lagrangian Floer homology of $M=\text{Sym}^g(\Sigma), L_0=\mathbb{T}_{\alpha},L_1=\mathbb{T}_{\beta}$?
Is Heegaard Floer homology the Lagrangian Floer homology of $M=\text{Sym}^g(\Sigma), L_0=\mathbb{T}_{\alpha},L_1=\mathbb{T}_{\beta}$? I am interested in the relationship between the theories
...
- 131
5
votes
2
answers
1k
views
Heegard diagrams for three-manifolds
I have a basic question about the Heegaard diagrams involved in providing a framework
for calculation of Floer-Homology of three-manifolds.
Typically such diagrams look like Figure 1 and Figure 2 here ...
- 5,976
3
votes
1
answer
223
views
Algebraic variations of the full knot Floer complex
In Hom's paper (arXiv link), p.20, Section 3.3 ends with
"There are other algebraic modifications one may consider, such as setting $U^n =
0$ or $UV = 0$",
referring to the knot Floer ...
- 171