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.



Does knot Floer homology detect knot genus in rational homology spheres?
Link Floer homology detects the Thurston norm, see [this paper](http://msp.org/gt/2009/13-5/gt-v13-n5-p09-s.pdf) by Yi Ni.


**EDIT**: There are some [lecture notes](http://arxiv.org/abs/1411.4540) 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.


