Thin links and Conway spheres

Artem Kotelskiy; Liam Watson; Claudius Zibrowius

doi:10.1112/s0010437x24007152

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arXiv · 2105.06308

Thin links and Conway spheres

Artem Kotelskiy·Liam Watson·Claudius Zibrowius

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Abstract

When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal $\delta$-grading. This leads to the broader class of thin links that one would like to characterize without reference to the invariant in question. We provide a relative version of thinness for tangles and use this to characterize thinness via tangle decompositions along Conway spheres. These results bear a strong resemblance to the L-space gluing theorem for three-manifolds with torus boundary. Our results are based on certain immersed curve invariants for Conway tangles, namely the Heegaard Floer invariant $\operatorname{HFT}$ and the Khovanov invariant $\operatorname{\widetilde{Kh}}$ that were developed by the authors in previous works.

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BibTeX RIS

Artem Kotelskiy, Liam Watson, Claudius Zibrowius. 2021-05-13. Thin links and Conway spheres. https://doi.org/10.1112/s0010437x24007152

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