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arXiv · 2610.20558

Minimal $\mathfrak{sl}_N$ Complexes of Rational Tangles via the Fukaya Category

Jonathan A. Higgins
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Abstract

We compute minimal $\mathfrak{sl}_N$ complexes for oriented rational tangles, denoted $[\![τ_{u/v}^{O}]\!]_N$, in terms of the topological Fukaya category of the $3$-punctured disk. This demonstrates that the complexes stabilize, allowing us to define a HOMFLY-PT homology for rational tangles.

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Jonathan A. Higgins. 2026-10-14. Minimal $\mathfrak{sl}_N$ Complexes of Rational Tangles via the Fukaya Category. https://arxiv.org/abs/2610.20558

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