9 citations · 31 across the 10 of their papers we have counts for
12 papers
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 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…
The correspondence induced on the pillowcase by the earring tangle
Guillem Cazassus, Christopher M. Herald, Paul Kirk +1
The earring tangle consists of four strands 4pt x [0,1] inside S^2 x [0,1] and one meridian around one of the strands. Equipping this tangle with a nontrivial SO(3) bundle, we show…
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…
Bordered theory for pillowcase homology
Artem Kotelskiy
We construct an algebraic version of Lagrangian Floer homology for immersed curves inside the pillowcase. We first associate to the pillowcase an algebra A. Then to an immersed cur…
Comparing homological invariants for mapping classes of surfaces
Artem Kotelskiy
We compare two different types of mapping class invariants: the Hochschild homology of an bimodule coming from bordered Heegaard Floer homology, and fixed point Floer co…
Minimal and Hamiltonian-minimal submanifolds in toric geometry
Artem Kotelskiy
In this paper we investigate a family of Hamiltonian-minimal Lagrangian submanifolds in , and other symplectic toric manifolds constructed from inte…