Lee filtration structure of torus links

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-Marengo...

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Bibliographic Details
Main Author Ren, Qiuyu
Format Journal Article
LanguageEnglish
Published 25.05.2023
Subjects
Mathematics - Geometric Topology
Mathematics - Quantum Algebra
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Summary: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.
DOI:10.48550/arxiv.2305.16089