# 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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