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

Abstract

We compute minimal ${\mathfrak{sl}}_N$ complexes for oriented rational tangles, denoted $[[{\tau }_{u/v}^O]{]}_N$, 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.

arXiv comment50 pages, many figures, 5 tables. Comments welcome!