53 citations · 177 across the 27 of their papers we have counts for
27 papers
Étude 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 posi…
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…
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…
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…
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…
On unknotting fibered positive knots and braids
Marc Kegel, Lukas Lewark, Naageswaran Manikandan +3
The unknotting number and the genus of braid positive knots are equal, as shown by Rudolph. We prove the stronger statement that any positive braid diagram of a genus k…
3-braid knots with maximal 4-genus
Sebastian Baader, Lukas Lewark, Filip Misev +1
We classify 3-braid knots whose topological 4-genus coincides with their Seifert genus, using McCoy's twisting method and the Xu normal form. In addition, we give upper bounds for…
Rasmussen invariants of Whitehead doubles and other satellites
Lukas Lewark, Claudius Zibrowius
We prove formulae for the -Rasmussen invariant of satellite knots of patterns with wrapping number 2, using the multicurve technology for Khovanov and Bar-Natan homol…
Quasipositivity and braid index of pretzel knots
Lukas Lewark
This short note is about three-stranded pretzel knots that have an even number of crossings in one of the strands. We calculate the braid index of such knots and determine which of…
On the values taken by slice torus invariants
Peter Feller, Lukas Lewark, Andrew Lobb
We study the space of slice-torus invariants. In particular we characterize the set of values that slice-torus invariants may take on a given knot in terms of the stable smooth sli…
Squeezed Knots
Peter Feller, Lukas Lewark, Andrew Lobb
Squeezed knots are those knots that appear as slices of genus-minimizing oriented smooth cobordisms between positive and negative torus knots. We show that this class of knots is l…
Khovanov homology and rational unknotting
Damian Iltgen, Lukas Lewark, Laura Marino
Building on 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 i…
Untwisting 3-strand torus knots
Sebastian Baader, Ian Banfield, Lukas Lewark
We prove that the signature bound for the topological 4-genus of 3-strand torus knots is sharp, using McCoy's twisting method. We also show that the bound is off by at most 1 for 4…
Balanced algebraic unknotting, linking forms, and surfaces in three- and four-space
Peter Feller, Lukas Lewark
We provide three 3-dimensional characterizations of the Z-slice genus of a knot, the minimal genus of a locally-flat surface in 4-space cobounding the knot whose complement has cyc…
Average four-genus of two-bridge knots
Sebastian Baader, Alexandra Kjuchukova, Lukas Lewark +2
We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of two-bridge knots tends to zero as the crossing number tends to infinity.
Almost positive links are strongly quasipositive
Peter Feller, Lukas Lewark, Andrew Lobb
We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive. This answers a question of Stoimenow's in the (strong) positive. As a second m…
Upsilon-like concordance invariants from sl(n) knot cohomology
Lukas Lewark, Andrew Lobb
We construct smooth concordance invariants of knots which take the form of piecewise linear maps from [0,1] to R, one for each n greater than or equal to 2. These invariants arise…
Checkerboard graph monodromies
Sebastian Baader, Lukas Lewark, Livio Liechti
We associate an open book with any connected plane checkerboard graph, thus providing a common extension of the classes of prime positive braid links and positive tree-like Hopf pl…
On classical upper bounds for slice genera
Peter Feller, Lukas Lewark
We introduce a new link invariant called the algebraic genus, which gives an upper bound for the topological slice genus of links. In fact, the algebraic genus is an upper bound fo…
Khovanov width and dealternation number of positive braid links
Sebastian Baader, Peter Feller, Lukas Lewark +1
We give asymptotically sharp upper bounds for the Khovanov width and the dealternation number of positive braid links, in terms of their crossing number. The same braid-theoretic t…
On the topological 4-genus of torus knots
Sebastian Baader, Peter Feller, Lukas Lewark +1
We prove that the topological locally flat slice genus of large torus knots takes up less than three quarters of the ordinary genus. As an application, we derive the best possible…
On calculating the slice genera of 11- and 12-crossing knots
Lukas Lewark, Duncan McCoy
This paper contains the results of efforts to determine values of the smooth and the topological slice genus of 11- and 12-crossing knots. Upper bounds for these genera were produc…
The stable 4-genus of alternating knots
Sebastian Baader, Lukas Lewark
We show that the difference between the genus and the stable topological 4-genus of alternating knots is either zero or at least 1/3.