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

Abstract: We show that any symplectically aspherical/Calabi-Yau filling of

Y : = p a r t i a l (V i m e s m a t h b b 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

m a t h r i n g W

is diffeomorphic to the interior of

V i m e s m a t h b b D

if

p i_{1} (Y)

is abelian and

d i m V g e 4

. And

W

is diffeomorphic to

V i m e s m a t h b b D

if moreover the Whitehead group of

p i_{1} (Y)

is trivial.

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