Holomorphic disks, link invariants and the multi-variable Alexander polynomial

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On combinatorial link Floer homology (2006, methodology): “ciated graded object, we get a group whose multi-graded Euler characteristic is the multi-variable Alexander polynomial of ~L, times a suitable normalization factor (this is proved in Equation (1) of [9], see also Theorem 6.1 below). We have endeavoured to separate the discussion of signs from the r”
Link Floer homology and the Thurston norm (2006, methodology): “Explicitly, this means that there is a nowhere vanishing one-form ω defined over S3−nd(L) representing the given cohomology class θ whose restriction to ∂nd(L) also vanishes nowhere.”
The decategorification of sutured Floer homology (2009, background): “Link Floer homology of a link L ⊂ S(3) was defined in [30].”
A cube of resolutions for knot Floer homology (2007, background): “K[ d(S,s) = X d,s (−1)d rkHFK[ d(S,−s). The indeterminacy of the M-grading is pinned down by actually ﬁxing the N-grading as follows. Consider the specialization of the complex to Ui= 1. According to [10], the resulting complex has the homology of a torus of dimension n− 1, which inherits the N-grad”