Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Lewark, Lukas"'
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 invariants and from torsion invariants. We also improve the bounds for the pro
Externí odkaz:
http://arxiv.org/abs/2409.05743
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 primeness of open books, which we consider to be of independent interest. Fo
Externí odkaz:
http://arxiv.org/abs/2408.15730
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 derive a surprising fact about torus knots that are met along the way o
Externí odkaz:
http://arxiv.org/abs/2405.13719
Autor:
Lewark, Lukas
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 coefficient of the Alexander polynomial have opposite sign. It follows that ce
Externí odkaz:
http://arxiv.org/abs/2402.03155
Autor:
Kegel, Marc, Lewark, Lukas, Manikandan, Naageswaran, Misev, Filip, Mousseau, Leo, Silvero, Marithania
The unknotting number $u$ and the genus $g$ of braid positive knots are equal, as shown by Rudolph. We prove the stronger statement that any positive braid diagram of a genus $g$ knot contains $g$ crossings, such that changing them produces a diagram
Externí odkaz:
http://arxiv.org/abs/2312.07339
Publikováno v:
Trans. Amer. Math. Soc. Ser. B 11 (2024), 600-621
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 the topological 4-genus of positive and strongly quasipositive 3-braid
Externí odkaz:
http://arxiv.org/abs/2303.11918
Autor:
Lewark, Lukas, Zibrowius, Claudius
We prove formulae for the $\mathbb{F}_2$-Rasmussen invariant of satellite knots of patterns with wrapping number 2, using the multicurve technology for Khovanov and Bar-Natan homology developed by Kotelskiy, Watson, and the second author. A new conco
Externí odkaz:
http://arxiv.org/abs/2208.13612
Autor:
Lewark, Lukas
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 them are quasipositive. The main tools are the Morton-Franks-Williams
Externí odkaz:
http://arxiv.org/abs/2205.05347
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society, Volume 176, Issue 1, January 2024, pp. 55 - 63
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 slice genus. Our study reveals that the resolution of the local Thom conj
Externí odkaz:
http://arxiv.org/abs/2202.13818
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 large and discuss how to obstruct squeezedness. The most effective obst
Externí odkaz:
http://arxiv.org/abs/2202.12289