Peculiar modules for 4‐ended tangles

@article{Zibrowius2020PeculiarMF,
  title={Peculiar modules for 4‐ended tangles},
  author={Claudius Zibrowius},
  journal={Journal of Topology},
  year={2020},
  volume={13}
}
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, 2011), we prove a glueing formula for this invariant which recovers link Floer homology HFL̂ . Moreover, we classify peculiar modules in terms of immersed curves on the 4‐punctured sphere. In fact, based on an algorithm of Hanselman, Rasmussen and Watson (Preprint, 2016, arXiv:1604.03466v2), we… 
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15 Citations
Highly Influential Citations
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Background Citations
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Methods Citations
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Results Citations
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15 Citations

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Heegaard Floer homology for manifolds with torus boundary: properties and examples
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The Fukaya category of the pillowcase, traceless character varieties, and Khovanov Cohomology
For a diagram of a 2-stranded tangle in the 3-ball we define a twisted complex of compact Lagrangians in the triangulated envelope of the Fukaya category of the smooth locus of the pillowcase. We…
On symmetries of peculiar modules; or, $\delta$-graded link Floer homology is mutation invariant
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…
Thin links and Conway spheres
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Immersed curves in Khovanov homology
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…
On a polynomial Alexander invariant for tangles and its categorification
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…
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Khovanov multicurves are linear
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…
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