• Corpus ID: 207796449

# 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}
}
• Published 31 October 2019
• Mathematics
• arXiv: Geometric Topology
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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On symmetries of peculiar modules, or $\delta$-graded link Floer homology is mutation invariant
We investigate symmetry properties of peculiar modules, a Heegaard Floer invariant of 4-ended tangles which the author introduced in [arXiv:1712.05050]. In particular, we give an almost complete
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