9 citations · 53 across the 17 of their papers we have counts for
17 papers
Benchmarks in Leipzig
Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg +45
Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the t…
On mutation invariance in Khovanov homology
Artem Kotelskiy, Liam Watson, Claudius Zibrowius
We show that reduced Khovanov homology over any field is invariant under component-preserving Conway mutation. Our proof relies on strong geography restrictions for a certain Khova…
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…
Heegaard Floer multicurves of double tangles
Claudius Zibrowius
We describe a simple formula for computing the Heegaard Floer multicurve invariant of double tangles from the Heegaard Floer multicurve invariant of knot complements. A comparison…
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…
Khovanov multicurves are linear
Artem Kotelskiy, Liam Watson, Claudius Zibrowius
In previous work we introduced a Khovanov multicurve invariant associated with Conway tangles. Applying ideas from homological mirror symmetry we sh…
Cosmetic operations and Khovanov multicurves
Artem Kotelskiy, Tye Lidman, Allison H. Moore +2
We prove an equivariant version of the Cosmetic Surgery Conjecture for strongly invertible knots. Our proof combines a recent result of Hanselman with the Khovanov multicurve invar…
Thin links and Conway spheres
Artem Kotelskiy, Liam Watson, Claudius Zibrowius
When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal -grading. This leads to the broader class of thin links that…
Khovanov homology and strong inversions
Artem Kotelskiy, Liam Watson, Claudius Zibrowius
There is a one-to-one correspondence between strong inversions on knots in the three-sphere and a special class of four-ended tangles. We compute the reduced Khovanov homology of s…
L-space knots have no essential Conway spheres
Tye Lidman, Allison H. Moore, Claudius Zibrowius
We prove that L-space knots do not have essential Conway spheres with the technology of peculiar modules, a Floer theoretic invariant for tangles.
A mnemonic for the Lipshitz-Ozsváth-Thurston correspondence
Artem Kotelskiy, Liam Watson, Claudius Zibrowius
When is a field, type D structures over the algebra are equivalent to immersed curves decorated with local systems in the twice-punctured disk.…
Khovanov invariants via Fukaya categories: the tangle invariants agree
Artem Kotelskiy, Liam Watson, Claudius Zibrowius
Given a pointed 4-ended tangle , there are two Khovanov theoretic tangle invariants, $\unicode{1044}_1(T)$ from [arXiv:1910.1458] and from [arXiv:1808.06957],…
Immersed curves in Khovanov homology
Artem Kotelskiy, Liam Watson, Claudius Zibrowius
We give a geometric interpretation of Bar-Natan's universal invariant for the class of tangles in the 3-ball with four ends: we associate with such 4-ended tangles multicurves…
On symmetries of peculiar modules; or, -graded link Floer homology is mutation invariant
Claudius Zibrowius
We investigate symmetry properties of peculiar modules, a Heegaard Floer invariant of 4-ended tangles which the author introduced in [arXiv:1712.05050]. In particular, we give an a…
Peculiar modules for 4-ended tangles
Claudius Zibrowius
With a 4-ended tangle , we associate a Heegaard Floer invariant , the peculiar module of . Based on Zarev's bordered sutured Heegaard Floer th…
On a Heegaard Floer theory for tangles
Claudius Zibrowius
The purpose of this thesis is to define a "local" version of Ozsváth and Szabó's Heegaard Floer homology for links in the 3-dimensional sphere, i.e.…
Kauffman states and Heegaard diagrams for tangles
Claudius Zibrowius
We define polynomial tangle invariants via Kauffman states and Alexander codes and investigate some of their properties. In particular, we prove symmetry relations for…