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arXiv · 2305.16089

Lee filtration structure of torus links

Qiuyu Ren
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Abstract

We determine the quantum filtration structure of the Lee homology of all torus links. In particular, this determines the $s$-invariant of a torus link equipped with any orientation. In the special case $T(n,n)$, our result confirms a conjecture of Pardon, as well as a conjecture of Manolescu-Marengon-Sarkar-Willis which establishes an adjunction-type inequality of the $s$-invariant for cobordisms in $k\overline{\mathbb{CP}^2}$. We also give a few applications of this adjunction inequality.

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Qiuyu Ren. 2023-05-25. Lee filtration structure of torus links. https://doi.org/10.2140/gt.2024.28.3935

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