A family of slice-torus invariants from the divisibility of Lee classes

Abstract

We give a family of slice-torus invariants ${\widetilde{ss}}_c$, each defined from the $c$-divisibility of the reduced Lee class in a variant of reduced Khovanov homology, parameterized by prime elements $c$ in any principal ideal domain $R$. For the special case $(R,c)=(F[H],H)$ where $F$ is any field, we prove that ${\widetilde{ss}}_c$ coincides with the Rasmussen invariant $s^F$ over $F$. Compared with the unreduced invariants $s{s}_c$ defined by the first author in a previous paper, we prove that $s{s}_c={\widetilde{ss}}_c$ for $(R,c)=(F[H],H)$ and $(\mathbb{Z},2)$. However for $(R,c)=(\mathbb{Z},3)$, computational results show that $s{s}_3$ is not slice-torus, which implies that it is linearly independent from the reduced invariants, and particularly from the Rasmussen invariants.

arXiv comment41 pages

References in corpus (15)

• Knot Floer homology and the four-ball genus
• Khovanov's homology for tangles and cobordisms
• Computations of the Ozsvath-Szabo knot concordance invariant
• Khovanov module and the detection of unlinks
• Gauge theory and Rasmussen's invariant
• A slice genus lower bound from sl(n) Khovanov-Rozansky homology
• Rasmussen's spectral sequences and the sl(N)-concordance invariants
• A refinement of Rasmussen's s-invariant
• A note on Gornik's perturbation of Khovanov-Rozansky homology
• Framed instanton homology and concordance
• The Bar-Natan homology and unknotting number
• Fixing the functoriality of Khovanov homology: a simple approach
• Slice-torus concordance invariants and Whitehead doubles of links
• Divisibility of Lee's class and its relation with Rasmussen's invariant
• On the values taken by slice torus invariants

Cited by in corpus (1)

• Involutive Khovanov homology and equivariant knots