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Link Floer homology categorifies the Conway function. (English) Zbl 1376.57004

Link Floer homology has two gradings, the Maslov grading and the Alexander grading. The Alexander grading is a relative grading in the original definition of link Floer homology based on Heegaard diagrams, while in the combinatorial definition based on grid diagrams (which is called grid homology in some literature) the ambiguity is removed so that the grading becomes an absolute one. It is well-known that the Euler characteristic of link Floer homology is the multi-variable Alexander polynomial of the given link, where the Alexander grading gives the power of the variables.
The Alexander polynomial of a link was first defined up to a power of the variables. Conway eliminated the indeterminacy by introducing the Conway function, which is the first known normalization of the Alexander polynomial. The main result of this paper states that the Conway function coincides with the Euler characteristic of the grid homology of a link.
To prove the main result, the authors construct and discuss the invariance of the Conway function by using the grid diagram of a link. Then they compare their construction with that of grid homology.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
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References:

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