Heegaard Floer multicurves of double tangles

Claudius Zibrowius

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arXiv · 2212.08501

Heegaard Floer multicurves of double tangles

Claudius Zibrowius

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Abstract

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 of Khovanov homology confirms that knot Floer homology and Khovanov homology behave very differently under satellite operations, echoing recent observations from arXiv:2208.13612. We also obtain a new characterisation of L-space knots in terms of Heegaard Floer A-link satellites. Along the way, we find the first example of a satellite knot whose knot Floer homology is thin.

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BibTeX RIS

Claudius Zibrowius. 2022-12-16. Heegaard Floer multicurves of double tangles. https://arxiv.org/abs/2212.08501

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