  Asaeda, Przytycki and Sikora defined a generalization of Khovanov homology
for links in $I$-bundles over compact surfaces. We prove that for a link
$L\subset (-1,1)\times T^2$, the Asaeda-Przytycki-Sikora homology of $L$ has
rank $2$ with $\mathbb{Z}/2$-coefficients if and only if $L$ is isotopic to an
embedded knot in $\{0\}\times T^2$.
