# Questions tagged [heegaard-floer-homology]

For questions about Heegaard-Floer homology (as introduced by Ozsváth-Szabó in 2003) and its uses in 3- and 4-dimensional topology.

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### Examples of counting holomorphic curves in cylindrical reformulation of Heegaard Floer

In 2005, Robert Lipshitz reformulated Heegaard Floer in a "cylindrical setting" by counting holomorphic curves in $\Sigma \times [0,1] \times \mathbb{R}$ where $\Sigma$ is a Heegaard surface ...
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### How to use a Heegaard diagram to retrieve the original 3-manifold that it represents?

(Disclaimer: I apologize that this is an introductory question for a forum like MathOverflow, but I have run out of ideas and resources to understand how this works, and I don't know where else to ask ...
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### 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 ...
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### Upsilon of an alternating knot

I have a couple of questions about how Oz-Stip-Sz computes the upsilon function invariant of an alternating knot in their upsilon ($\Upsilon$) paper here.1 This is theorem 1.14 (on the bottom of page ...
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### base point in Heegaard Floer homology

It is stated in Mcduff's overview paper "FLOER THEORY AND LOW DIMENSIONAL TOPOLOGY", end of page 9, that the Heegaard Floer homology without considering a base point depends only on the homology of ...
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### What is the Heegaard Floer Homology of a connect sum of $S^2 \times S^1$s?

There are many conjecturally-equivalent three-manifold Floer homologies, of which my understanding is the most-computable is Heegaard Floer homology. What is the (Heegaard) Floer homology of a ...
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### Admissibility in Heegaard Floer, especially with torsion Spin^c structures

I'm confused about the relationship between strong admissibility and weak admissibility for pointed diagrams in Heegaard Floer theory. For reference, here are Ozsváth-Szàbo's original definitions: ...
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### Is there a reasonable definition of TQFTs for n-cobordisms with connected inputs/outputs?

A question that's been on my mind for a while is whether any precise statement to the effect of "Heegaard Floer homology is a TQFT," for some reasonable definition of TQFT, can be made. Of course, a ...
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### Untwisting Heegaard diagrams

Most Heegaard diagrams contain many rectangles, for instance from loops that circle around one of the handle disks. You can always `twist' a Heegaard diagram to get more and more rectangles (as in ...
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### On the proof of Robert Lipshitz's formula on Maslov index.

Hello. I am a beginning graduate student who wants to study Heegaard Floer Homologies. I am now reading the paper https://arxiv.org/abs/1301.4919 Errata to 'A cylindrical reformulation of Heegaard ...
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### maslov index of a holomorphic disk

I am studying some introductory papers on heegard floer homology and I do not understand the meaning of the Maslov index of a holomorphic disk. I could not find any definition in any of the papers. I ...
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### Decorations in Szabo's combinatorial spectral sequence

Szabo in http://arxiv.org/abs/1010.4252 gives a combinatorial candidate for what an explicit calculation of the spectral sequence of branched double covers should yield. In other words he gives a ...
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### heegard diagram

It seems like there is an algorithm to find the Heegard diagram of a 3 manifold obtained by surgery on a link. Also someone told me I can find it in the Gompf and Stipciz's book. But I could not find ...
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### Heegard Floer homology [closed]

I am new to Heegard Floer. So far I understand that different HF groups are invariants of a three manifold. But I do not understand what these groups actually measure. I mean it seems to me that they ...
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### Sarkar's Maslov index formula

I have difficulty understanding Sarkar's maslov index formula in symmetric products from http://arxiv.org/abs/math/0609673. If $D$ is an $n$-sided region with corner points $p_1,\ldots, p_n$ then it ...
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### 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 ...
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### Wanted: differential coming from higher genus surface in Heegaard Floer homology

I am interested in studying moduli of complex surfaces which arise in computing the differential on the Heegaard Floer homology chain complex. In particular, I am interested in the generic case, when ...
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