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arXiv · 2502.02939

Combinatorial knot Floer homology and tangle decompositions

Hajime Kubota
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Abstract

We partially determine grid homology (combinatorial knot Floer homology) of diagonal knots, which are conjectured to be equivalent to positive braid knots, by exploiting nice grid diagrams. Its next-to-top term detects the number of prime factors, and the $\text{top}-2$ term corresponds to the decompositions of the knot into two non-integer tangles. We compare diagonal knots to various classes of knots, such as positive braids, fibered positive knots, and $L$-space knots.

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Hajime Kubota. 2025-02-05. Combinatorial knot Floer homology and tangle decompositions. https://arxiv.org/abs/2502.02939

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