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We give a family of slice-torus invariants $\tilde{ss}_c$, each defined fromthe $c$-divisibility of the reduced Lee class in a variant of reduced Khovanovhomology, 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 provethat $\tilde{ss}_c$ coincides with the Rasmussen invariant $s^F$ over $F$.Compared with the unreduced invariants $ss_c$ defined by the first author in aprevious paper, we prove that $ss_c = \tilde{ss}_c$ for $(R, c) = (F[H], H)$and $(\mathbb{Z}, 2)$. However for $(R, c) = (\mathbb{Z}, 3)$, computationalresults show that $ss_3$ is not slice-torus, which implies that it is linearlyindependent from the reduced invariants, and particularly from the Rasmusseninvariants.

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