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Algebraic Variationsvariations of the Full Knotfull knot Floer Complexcomplex

In Hom's paper https://arxiv.org/pdf/2008.01836.pdf(arXiv link), p.20, sectionSection 3.3 ends with

"There are other algebraic modifications one may consider, such as setting $U^n = 0$ or $UV = 0$,"

"There are other algebraic modifications one may consider, such as setting $U^n = 0$ or $UV = 0$",

referring to the Knotknot Floer Homologyhomology with $\mathbb{F}[U,V]$ coefficients. That is, we consider pseudoholomorphic disks in the Heegaard diagram (or rather, in the symmetric product of the Heegaard surface), including those passing through both basepoints $w$ and $z$.

However, there is no reference to works that do consider these different variations. My first question is, which modifications have already been considered/published, and for each what is a good reference?

The second question is similar to the first: in the specific example that we set say $U^2=0$, is there a good geometric interpretation of what kind of information we're losing?

Algebraic Variations of the Full Knot Floer Complex

In Hom's paper https://arxiv.org/pdf/2008.01836.pdf, 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 Homology with $\mathbb{F}[U,V]$ coefficients. That is, we consider pseudoholomorphic disks in the Heegaard diagram (or rather, in the symmetric product of the Heegaard surface), including those passing through both basepoints $w$ and $z$.

However, there is no reference to works that do consider these different variations. My first question is, which modifications have already been considered/published, and for each what is a good reference?

The second question is similar to the first: in the specific example that we set say $U^2=0$, is there a good geometric interpretation of what kind of information we're losing?

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 homology with $\mathbb{F}[U,V]$ coefficients. That is, we consider pseudoholomorphic disks in the Heegaard diagram (or rather, in the symmetric product of the Heegaard surface), including those passing through both basepoints $w$ and $z$.

However, there is no reference to works that do consider these different variations. My first question is, which modifications have already been considered/published, and for each what is a good reference?

The second question is similar to the first: in the specific example that we set say $U^2=0$, is there a good geometric interpretation of what kind of information we're losing?

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Algebraic Variations of the Full Knot Floer Complex

In Hom's paper https://arxiv.org/pdf/2008.01836.pdf, 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 Homology with $\mathbb{F}[U,V]$ coefficients. That is, we consider pseudoholomorphic disks in the Heegaard diagram (or rather, in the symmetric product of the Heegaard surface), including those passing through both basepoints $w$ and $z$.

However, there is no reference to works that do consider these different variations. My first question is, which modifications have already been considered/published, and for each what is a good reference?

The second question is similar to the first: in the specific example that we set say $U^2=0$, is there a good geometric interpretation of what kind of information we're losing?