• Corpus ID: 218516781

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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Linear independence of rationally slice knots
A knot in $S^3$ is rationally slice if it bounds a disk in a rational homology ball. We give an infinite family of rationally slice knots that are linearly independent in the knot concordance group.…

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