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My question is the following:

Does knot Floer homology detect the genus of null-homologous knot in rational homology spheres?

If the answer is yes, I would like to have a reference for the statement of the result and the proof.

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Link Floer homology detects the Thurston norm, see this paper by Yi Ni.

EDIT: There are some lecture notes that Robert Lipshitz just put up on the arXiv, where he discusses the problem you're interested in. I haven't had time to look carefully into them, but he's usually very careful and clear in what he writes.

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