Instantons and Khovanov homology in ℝℙ³

Yang, Hongjian

doi:10.1090/tran/9405

Instantons and Khovanov homology in $\mathbb {RP}^3$
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by Hongjian Yang;

Trans. Amer. Math. Soc. 378 (2025), 4991-5009

DOI: https://doi.org/10.1090/tran/9405

Published electronically: March 4, 2025

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Abstract:

We study the instanton Floer homology for links in $\mathbb {RP}^3$ and prove that the second page of Kronheimer–Mrowka’s spectral sequence is isomorphic to the Khovanov homology of the mirror link. As an application, we prove that Khovanov homology detects the unknot and the standard $\mathbb {RP}^1$ in $\mathbb {RP}^3$.

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Instantons and Khovanov homology in $\mathbb {RP}^3$
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Abstract: