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

We compute minimal ${\mathfrak{s}\mathfrak{l}}_N$ complexes for oriented rational tangles, denoted $[\text{\hspace{0.17em}⁣}[{\tau }_{u\mathrm{/}v}^O]\text{\hspace{0.17em}⁣}{]}_N$, 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.