# Khovanov invariants via Fukaya categories: the tangle invariants agree

@article{Kotelskiy2020KhovanovIV, title={Khovanov invariants via Fukaya categories: the tangle invariants agree}, author={Artem Kotelskiy and Liam Watson and Claudius Zibrowius}, journal={arXiv: Geometric Topology}, year={2020} }

Given a pointed 4-ended tangle $T \subset D^3$, there are two Khovanov theoretic tangle invariants, $\unicode{1044}_1(T)$ from [arXiv:1910.1458] and $L_T$ from [arXiv:1808.06957], which are twisted complexes over the Fukaya category of the boundary 4-punctured sphere $(S^2,4\text{pt})=\partial (D^3, T)$. We prove that these two invariants are the same.

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