Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Zibrowius, Claudius"'
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
Autor:
Zibrowius, Claudius
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 with a similar multicurve invariant for Conway tangles in the setting
Externí odkaz:
http://arxiv.org/abs/2212.08501
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
In previous work we introduced a Khovanov multicurve invariant $\operatorname{\widetilde{Kh}}$ associated with Conway tangles. Applying ideas from homological mirror symmetry we show that $\operatorname{\widetilde{Kh}}$ is subject to strong geography
Externí odkaz:
http://arxiv.org/abs/2202.01460
Publikováno v:
Math. Ann. 389 (2023) 2903-2930
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 invariants $\widetilde{\operatorname{Kh}}$ and $\widetilde{\operatorname{BN
Externí odkaz:
http://arxiv.org/abs/2109.14049
Publikováno v:
Compositio Math. 160 (2024) 1467-1524
When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal $\delta$-grading. This leads to the broader class of thin links that one would like to characterize without reference to the invariant
Externí odkaz:
http://arxiv.org/abs/2105.06308
Publikováno v:
Open Book Series 5 (2022) 223-244
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 such tangles for all strong inversions on knots with up to 9 crossings,
Externí odkaz:
http://arxiv.org/abs/2104.13592
Publikováno v:
Geom. Topol. 26 (2022) 2065-2102
We prove that L-space knots do not have essential Conway spheres with the technology of peculiar modules, a Floer theoretic invariant for tangles.
Comment: 25 pages, 11 color figures created with PSTricks and TikZ. v1: Comments welcome! v2: This
Comment: 25 pages, 11 color figures created with PSTricks and TikZ. v1: Comments welcome! v2: This
Externí odkaz:
http://arxiv.org/abs/2006.03521
Publikováno v:
Algebr. Geom. Topol. 23 (2023) 2519-2543
When $\mathbf{k}$ is a field, type D structures over the algebra $\mathbf{k}[u,v]/(uv)$ are equivalent to immersed curves decorated with local systems in the twice-punctured disk. Consequently, knot Floer homology, as a type D structure over $\mathbf
Externí odkaz:
http://arxiv.org/abs/2005.02792
Given a pointed 4-ended tangle $T \subset D^3$, there are two Khovanov theoretic tangle invariants, $\unicode{1044}_1(T)$ from [arXiv:1910.1458] and $L_T$ from [arXiv:1808.06957], which are twisted complexes over the Fukaya category of the boundary 4
Externí odkaz:
http://arxiv.org/abs/2004.01619