On filings of $\mathrm{\partial }(V\times \mathbb{D})$

We show that any symplectically aspherical/Calabi-Yau filling of $Y:=\mathrm{\partial }(V\times \mathbb{D})$ 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}$$ifmoreovertheWhiteheadgroupof$\pi_1(Y)$ is trivial.