Lee filtration structure of torus links

Ren, Qiuyu¹

¹ Department of Mathematics, University of California, Berkeley, Berkeley, CA, United States

Geometry & topology, Tome 28 (2024) no. 8, pp. 3935-3960.

Résumé

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 $k{\overline{ℂ\mathbb{P}}}^2$. We also give a few applications of this adjunction inequality.

Détail

DOI : 10.2140/gt.2024.28.3935

Keywords: torus links, Lee homology, adjunction inequality, $s$–invariant, Khovanov homology

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