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math.GT2025
Smoothly slice knots with Alexander polynomial 1 and high unknotting number
Lukas Lewark
We prove the existence of a smoothly doubly slice, amphicheiral knot with Alexander polynomial 1 and unknotting number 5.
math.GT2024
The second coefficient of the Alexander polynomial as a satellite obstruction
Lukas Lewark
A set L of links is introduced, containing positive braid links as well as arborescent positive Hopf plumbings. It is shown that for links in P, the leading and the second coeffici…
math.GT2024
Khovanov homology and refined bounds for Gordian distances
Lukas Lewark, Laura Marino, Claudius Zibrowius
From Khovanov homology, we extract a new lower bound for the Gordian distance of knots, which combines and strengthens the previously existing bounds coming from Rasmussen invarian…