# A mnemonic for the Lipshitz-Ozsv\'ath-Thurston correspondence.

@article{Kotelskiy2020AMF, title={A mnemonic for the Lipshitz-Ozsv\'ath-Thurston correspondence.}, author={Artem Kotelskiy and Liam Watson and Claudius Zibrowius}, journal={arXiv: Geometric Topology}, year={2020} }

When $\mathbf{k}$ is a field, type D structures over the algebra $\mathbf{k}[u,v]/(uv)$ are equivalent to immersed curves decorated with local systems in the twice-punctured disk. Consequently, knot Floer homology, as a type D structure over $\mathbf{k}[u,v]/(uv)$, can be viewed as a set of immersed curves. With this observation as a starting point, given a knot $K$ in $S^3$, we realize the immersed curve invariant $\widehat{\mathit{HF}}(S^3 \setminus \mathring{\nu}(K))$ [arXiv:1604.03466] by…

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