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

Abstract

We give a family of slice-torus invariants, one defined for each prime element $c$ in a principal ideal domain $R$, from the $c$-divisibility of the reduced Lee class in a variant of reduced Khovanov homology. It is proved that this family contains the Rasmussen invariant $s^F$ over any field $F$. Moreover, computational results show that the invariants corresponding to $(R, c) = (\mathbb{Z}, 2)$, $(\mathbb{Z}, 3)$ and $(\mathbb{Z}[i], 1 + i)$ are distinct from $s^\mathbb{Q}$.Comment: 38 page