We show that any symplectically aspherical/Calabi-Yau filling of $Y:=\partial(V\times \mathbb{ D})$ has vanishing symplectic cohomology for any Liouville domain $V$. In particular, we make no topological requirement on the filling and $c_1(V)$ can be nonzero. Moreover, we show that for any symplectically aspherical/Calabi-Yau filling $W$ of $Y$, the interior $\mathring{ W}$ is diffeomorphic to the interior of $V\times \mathbb{ D}$ if $\pi_1(Y)$ is abelian and $\dim V\ge 4$. And $W$ is diffeomorphic to $V\times \mathbb{ D}$ if moreover the Whitehead group of $\pi_1(Y)$ is trivial.
Categories: math.SG