Khovanov homology detects split links

Robert Lipshitz; Sucharit Sarkar

doi:10.1353/ajm.2022.0043

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arXiv · 1910.04246

Khovanov homology detects split links

Robert Lipshitz·Sucharit Sarkar

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Abstract

Extending ideas of Hedden-Ni, we show that the module structure on Khovanov homology detects split links. We also prove an analogue for untwisted Heegaard Floer homology of the branched double cover. Technical results proved along the way include two interpretations of the module structure on untwisted Heegaard Floer homology in terms of twisted Heegaard Floer homology and the fact that the module structure on the reduced Khovanov complex of a link is well-defined up to quasi-isomorphism.

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Robert Lipshitz, Sucharit Sarkar. 2019-10-09. Khovanov homology detects split links. https://doi.org/10.1353/ajm.2022.0043

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