Lee filtration structure of torus links

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-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.

arXiv comment22 pages, 4 figures in color; final version, to appear in Geometry and Topology

References in corpus (8)

• Knot Floer homology and the four-ball genus
• Khovanov's homology for tangles and cobordisms
• On Khovanov's categorification of the Jones polynomial
• A spectral sequence for Khovanov homology with an application to (3,q)-torus links
• Homological thickness and stability of torus knots
• Annular Khovanov homology and knotted Schur-Weyl representations
• The link concordance invariant from Lee homology
• Embedding surfaces in 4-manifolds

Cited by in corpus (1)

• An RBG construction of integral surgery homeomorphisms