Immersed curves in Khovanov homology
A Kotelskiy, L Watson, C Zibrowius - arXiv preprint arXiv:1910.14584, 2019 - arxiv.org
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 $ T $ multicurves …
in the 3-ball with four ends: we associate with such 4-ended tangles $ T $ multicurves …
Peculiar modules for 4‐ended tangles
C Zibrowius - Journal of Topology, 2020 - Wiley Online Library
With a 4‐ended tangle T, we associate a Heegaard Floer invariant CFT∂(T), the peculiar
module of T. Based on Zarev's bordered sutured Heegaard Floer theory (Zarev, PhD Thesis …
module of T. Based on Zarev's bordered sutured Heegaard Floer theory (Zarev, PhD Thesis …
Doubled Khovanov Homology
W Rushworth - Canadian Journal of Mathematics, 2018 - cambridge.org
We define a homology theory of virtual links built out of the direct sum of the standard
Khovanov complex with itself, motivating the name doubled Khovanov homology. We …
Khovanov complex with itself, motivating the name doubled Khovanov homology. We …
Categorification and dynamics in generalised braid groups
EXC Heng - 2022 - search.proquest.com
Recent developments in the theory of stability conditions and its relation to Teichmuller
theory have revealed a deep connection between triangulated categories and surfaces …
theory have revealed a deep connection between triangulated categories and surfaces …
Introduction to stability conditions and its relation to the conjecture for Artin groups
E Heng - arXiv preprint arXiv:2404.11562, 2024 - arxiv.org
arXiv:2404.11562v1 [math.GR] 17 Apr 2024 Page 1 INTRODUCTION TO STABILITY
CONDITIONS AND ITS RELATION TO THE K(π,1) CONJECTURE FOR ARTIN GROUPS …
CONDITIONS AND ITS RELATION TO THE K(π,1) CONJECTURE FOR ARTIN GROUPS …
Thin links and Conway spheres
A Kotelskiy, L Watson, C Zibrowius - Compositio Mathematica, 2024 - cambridge.org
Thin links and Conway spheres Page 1 Thin links and Conway spheres Artem Kotelskiy,
Liam Watson and Claudius Zibrowius Compositio Math. 160 (2024), 1467–1524. doi:10.1112/S0010437X24007152 …
Liam Watson and Claudius Zibrowius Compositio Math. 160 (2024), 1467–1524. doi:10.1112/S0010437X24007152 …
The Khovanov homology of alternating virtual links
H Karimi - Michigan Mathematical Journal, 2021 - projecteuclid.org
In this paper, we study the Khovanov homology of an alternating virtual link L and show that
it is supported on g+ 2 diagonal lines, where g equals the virtual genus of L. Specifically, we …
it is supported on g+ 2 diagonal lines, where g equals the virtual genus of L. Specifically, we …
Homotopy-Theoretic Studies of Khovanov-Rozansky Homology
H Becker - 2015 - bonndoc.ulb.uni-bonn.de
This dissertation applies homotopy-theoretic methods to the study of Khovanov-Rozansky
homology, a generalization of Khovanov homology (which in turn categorifies the Jones …
homology, a generalization of Khovanov homology (which in turn categorifies the Jones …
Additional gradings on generalizations of Khovanov homology and invariants of embedded surfaces
VO Manturov, W Rushworth - Journal of Knot Theory and Its …, 2018 - World Scientific
We define additional gradings on two generalizations of Khovanov homology (one due to
the first author, the other due to the second), and use them to define invariants of various …
the first author, the other due to the second), and use them to define invariants of various …
Khovanov invariants via Fukaya categories: the tangle invariants agree
A Kotelskiy, L Watson, C Zibrowius - arXiv preprint arXiv:2004.01619, 2020 - arxiv.org
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 …
invariants, $\unicode {1044} _1 (T) $ from [arXiv: 1910.1458] and $ L_T $ from [arXiv …