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 $\mathbb {RP}^3$.References
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Bibliographic Information
- Hongjian Yang
- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
- MR Author ID: 1605667
- ORCID: 0000-0001-8539-5985
- Email: yhj@stanford.edu
- Received by editor(s): March 3, 2024
- Received by editor(s) in revised form: November 6, 2024, and December 31, 2024
- Published electronically: March 4, 2025
- © Copyright 2025 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 4991-5009
- MSC (2020): Primary 57K18; Secondary 57R58
- DOI: https://doi.org/10.1090/tran/9405