Khovanov invariants via Fukaya categories: the tangle invariants agree

Abstract

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.

14 pages, 11 figures, uses TikZ and PSTricks. C++ program provided via ancillary files. Comments welcome!

References in corpus (1)

• Immersed curves in Khovanov homology