Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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