Khovanov homology and the cinquefoil

  • John A. Baldwin

    Boston College, Chestnut Hill, USA
  • Ying Hu

    University of Nebraska Omaha, Omaha, USA
  • Steven Sivek

    Imperial College London, London, UK
Khovanov homology and the cinquefoil cover
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Abstract

We prove that Khovanov homology with coefficients in detects the torus knot. Our proof makes use of a wide range of deep tools in Floer homology, Khovanov homology, and Khovanov homotopy. We combine these tools with classical results on the dynamics of surface homeomorphisms to reduce the detection question to a problem about mutually braided unknots, which we then solve with computer assistance.

Cite this article

John A. Baldwin, Ying Hu, Steven Sivek, Khovanov homology and the cinquefoil. J. Eur. Math. Soc. 27 (2025), no. 6, pp. 2443–2465

DOI 10.4171/JEMS/1415