# Immersed curves in Khovanov homology

@article{Kotelskiy2019ImmersedCI, title={Immersed curves in Khovanov homology}, author={Artem Kotelskiy and Liam Watson and Claudius Zibrowius}, journal={arXiv: Geometric Topology}, year={2019} }

We give a geometric interpretation of Bar-Natan's universal invariant for the class of tangles in the 3-ball with four ends: we associate with such 4-ended tangles $T$ multicurves $\widetilde{\operatorname{BN}}(T)$, that is, collections of immersed curves with local systems in the 4-punctured sphere. These multicurves are tangle invariants up to homotopy of the underlying curves and equivalence of the local systems. They satisfy a gluing theorem which recovers the reduced Bar-Natan homology of…

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## 13 Citations

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The right-hand side of the card indicates how the Rasmussen invariants are computed, using the multicurve techniques of [2], from a decomposition of K into the tangles T1 and T2. The non-compact…

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