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

Abstract

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.

Added more details and corrected many typos. Comments welcome!

References in corpus (2)

• The Kunneth formula in Floer homology for manifolds with restricted contact type boundary
• $({\mathbb{RP}}^{2n-1},{\xi }_{std})$ is not exactly fillable for $n\ne 2^k$

Cited by in corpus (3)

• On fillings of contact links of quotient singularities
• Connected sums of Brieskorn contact $5$-spheres
• A landscape of contact manifolds via rational SFT