We examine the relationship between the oriented cube of resolutions for knot Floer homology and HOMFLY-PT homology. By using a filtration induced by additional basepoints on the Heegaard diagram for a knot [Formula: see text], we see that the filtered complex decomposes as a direct sum of HOMFLY-PT complexes of various subdiagrams. Applying Jaeger’s composition product formula for knot polynomials, we deduce that the graded Euler characteristic of this direct sum is the HOMFLY-PT polynomial of [Formula: see text].

中文翻译：

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结Floer立方体分辨率和组合产品

我们研究了结 Floer 同源性和 HOMFLY-PT 同源性的定向分辨率立方体之间的关系。通过对结使用由 Heegaard 图上的附加基点引起的过滤[公式：见文本]，我们看到过滤后的复合体分解为各种子图的 HOMFLY-PT 复合体的直接和。应用结多项式的Jaeger合成积公式，我们推导出这个直接和的分级欧拉特征是[公式：见正文]的HOMFLY-PT多项式。