Khovanov homology and rational unknotting

  • Damian Iltgen

    University of Regensburg, Germany
  • Lukas Lewark

    University of Regensburg, Germany
  • Laura Marino

    Université Paris Cité, France
Khovanov homology and rational unknotting cover
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Abstract

Building on the work by Alishahi–Dowlin, we extract a new knot invariant from universal Khovanov homology. While is a lower bound for the unknotting number, in fact more is true: is a lower bound for the proper rational unknotting number (the minimal number of rational tangle replacements preserving connectivity necessary to relate a knot to the unknot). Moreover, we show that, for all , there exists a knot with . Along the way, following Thompson, we compute the Bar-Natan complexes of rational tangles.

Cite this article

Damian Iltgen, Lukas Lewark, Laura Marino, Khovanov homology and rational unknotting. Quantum Topol. 16 (2025), no. 4, pp. 655–741

DOI 10.4171/QT/244