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 $(R,c)=\left(F\right[H],H)$ 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 $(R,c)=\left(F\right[H],H)$ and $(Z,2)$. However for $(R,c)=(Z,3)$, 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.