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Lee filtration structure of torus links

Qiuyu Ren

Geometry & Topology 28 (2024) 3935–3960
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 and Willis which establishes an adjunction-type inequality of the s–invariant for cobordisms in k¯2. We also give a few applications of this adjunction inequality.

Keywords
torus links, Lee homology, adjunction inequality, $s$–invariant, Khovanov homology
Mathematical Subject Classification
Primary: 57K18
Secondary: 57K10, 57K40
References
Publication
Received: 25 May 2023
Revised: 11 December 2023
Accepted: 19 January 2024
Published: 20 December 2024
Proposed: Ciprian Manolescu
Seconded: András I Stipsicz, Peter Ozsváth
Authors
Qiuyu Ren
Department of Mathematics
University of California, Berkeley
Berkeley, CA
United States

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