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.

41 pages

References in corpus (3)

• Framed instanton homology and concordance
• Fixing the functoriality of Khovanov homology: a simple approach
• On the values taken by slice torus invariants

Cited by in corpus (1)

• Involutive Khovanov homology and equivariant knots