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arXiv · 1508.03037

The Knot Floer Cube of Resolutions and the Composition Product

Nathan Dowlin
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Abstract

We examine the relationship between the (untwisted) knot Floer cube of resolutions and HOMFLY-PT homology. By using a filtration induced by additional basepoints on the Heegaard diagram for a knot $K$, we see that the filtered complex decomposes as a direct sum of HOMFLY-PT homologies of various subdiagrams. Jaeger's composition product formula shows that the graded Euler characteristic of this direct sum is the HOMFLY-PT polynomial of $K$.

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Nathan Dowlin. 2015-08-12. The Knot Floer Cube of Resolutions and the Composition Product. https://arxiv.org/abs/1508.03037

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