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Peculiar modules for 4‐ended tangles

- Claudius Zibrowius
- MathematicsJournal of Topology
- 13 December 2017

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, Columbia University,… Expand

ON SYMMETRIES OF PECULIAR MODULES or δ-GRADED LINK FLOER HOMOLOGY IS MUTATION INVARIANT

- Claudius Zibrowius
- Mathematics
- 2019

We investigate symmetry properties of peculiar modules, a Heegaard Floer invariant of 4-ended tangles which the author introduced in [Zib20]. In particular, we give an almost complete answer to the… Expand

On a Heegaard Floer theory for tangles

- Claudius Zibrowius
- Mathematics
- 24 October 2016

The purpose of this thesis is to define a "local" version of Ozsv\'{a}th and Szab\'{o}'s Heegaard Floer homology $\operatorname{\widehat{HFL}}$ for links in the 3-dimensional sphere, i.e. a Heegaard… Expand

On a polynomial Alexander invariant for tangles and its categorification

- Claudius Zibrowius
- Mathematics
- 19 January 2016

We generalise the Kauffman state formula for the classical multivariate Alexander polynomial of knots and links to tangles and thereby obtain a finite set of polynomial tangle invariants. In the… Expand

Immersed curves in Khovanov homology

- Artem Kotelskiy, Liam Watson, Claudius Zibrowius
- Mathematics
- 31 October 2019

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… Expand

Kauffman states and Heegaard diagrams for tangles

- Claudius Zibrowius
- MathematicsAlgebraic & Geometric Topology
- 19 January 2016

We define polynomial tangle invariants $\nabla_T^s$ via Kauffman states and Alexander codes and investigate some of their properties. In particular, we prove symmetry relations for $\nabla_T^s$ of… Expand

Khovanov invariants via Fukaya categories: the tangle invariants agree

- Artem Kotelskiy, Liam Watson, Claudius Zibrowius
- Mathematics
- 3 April 2020

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… Expand

On symmetries of peculiar modules, or $\delta$-graded link Floer homology is mutation invariant

- Claudius Zibrowius
- MathematicsJournal of the European Mathematical Society
- 10 September 2019

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 almost complete… Expand

Khovanov multicurves are linear

- Artem Kotelskiy, Liam Watson, Claudius Zibrowius
- Mathematics
- 3 February 2022

In previous work we introduced a Khovanov multicurve invariant K̃h associated with Conway tangles. Applying ideas from homological mirror symmetry we show that K̃h is subject to strong geography… Expand

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