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Khovanov Homology and Rational Unknotting by Iltgen, Damian; Lewark, Lukas; Marino, Laura is a scholarly article available to read on EtoBox.

What is Khovanov Homology and Rational Unknotting about?

Building on work by Alishahi-Dowlin, we extract a new knot invariant $\lambda \ge 0$ from universal Khovanov homology. While $\lambda$ is a lower bound for the unknotting number, in fact more is true: $\lambda$ 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 $n \ge 0$, there exists a knot K with $\lambda(K) = n$. Along the way, following Thompson, we compute the Bar-Natan complexes of rational tangles.

Author

Iltgen, Damian; Lewark, Lukas; Marino, Laura

Published

2021

Language

EN