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 r …

Hello. I am a beginning graduate student who wants to study Heegaard Floer Homologies. I am now reading the paper http://front.math.ucdavis.edu/1301.4919 Errata to 'A cylindrica …

I would like to collect a list of applications of Heegaard-Floer theory. By applications, I don't mean things like "it can detect the unknot" or "it can detect knot genus". Algor …

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 …

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. B …

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 a …

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 se …

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,\ …

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. …

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 th …

In order to define Heegaard Floer Homology for a connected, closed, oriented 3 manifold, we fix a generic path of nearly symmetric almost complex strucutre $J_s$ over $Sym^g(\Sigma …

The $g$-fold symmetric product of a Riemann surface of genus $g$ naturally has both a symplectic structure as well as a complex structure. Is it in fact Calabi-Yau? If so, is any …

Recently, the Seiberg-Witten-Floer homology created by Kronheimer and Mrowka has important applications in Taubes' proofs of Weinstein conjecture and Arnold Chord Conjecture. Also, …