7 papers
Ãtude on the Delta-unknotting number
Sebastian Baader, Lukas Lewark
We derive an almost sharp lower bound on the Casson invariant of positive braid knots. As a consequence, we show that the -unknotting number is quasi-additive on the set of pos…
The Conway knot has infinite concordance order
Chiara Donatone, Marc Kegel, Lukas Lewark +1
We examine how the Rasmussen invariant, satellite operations, and null-homologous twists can be used to establish infinite order of knots in the smooth concordance group. As an app…
Signs of knot polynomial evaluations from a topological perspective
Luana Jost, Lukas Lewark
We prove that for knots, the evaluation of the Jones polynomial at the sixth root of unity, as well as the evaluation of the -polynomial at the reciprocal of the golden ratio, a…
Homogeneous braids are visually prime
Peter Feller, Lukas Lewark, Miguel Orbegozo Rodriguez
We show that closures of homogeneous braids are visually prime, addressing a question of Cromwell. The key technical tool for the proof is the following criterion concerning primen…
Monodromies of surfaces in 3-manifolds, right-veeringness, and primeness of links
Peter Feller, Lukas Lewark, Miguel Orbegozo Rodriguez
Extending the notion of monodromies associated with open books of -manifolds, we consider monodromies for all incompressible surfaces in -manifolds as partial self-maps of th…
Minimal cobordisms between thin and thick torus knots
Sebastian Baader, Lukas Lewark, Filip Misev +1
We determine the locally flat cobordism distance between torus knots with small and large braid index, up to high precision. Here small means 2, 3, 4, or 6. As an application, we d…