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-Mar...

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Bibliographic Details
Published inarXiv.org
Main Author Ren, Qiuyu
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.01.2024
Subjects
Filtration
Homology
Invariants
Toruses
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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.
ISSN:2331-8422