Lee filtration structure of torus links

Ren, Qiuyu

doi:10.2140/gt.2024.28.3935

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Lee filtration structure of torus links

Qiuyu Ren

Geometry & Topology 28 (2024) 3935–3960

DOI: 10.2140/gt.2024.28.3935

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 $k {\bar{ℂ ℙ}}^{2}$ . 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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Volume 28, issue 8 (2024)