  We consider exact fillings with vanishing first Chern class of asymptotically
dynamically convex (ADC) manifolds. We construct two structure maps on the
positive symplectic cohomology and prove that they are independent of the
filling for ADC manifolds. The invariance of the structure maps implies that
the vanishing of symplectic cohomology and the existence of symplectic
dilations are properties independent of the filling for ADC manifolds. Using
them, various topological applications on symplectic fillings are obtained,
including the uniqueness of diffeomorphism types of fillings for many contact
manifolds. We use the structure maps to define the first symplectic
obstructions to Weinstein fillability. In particular, we show that for all
dimension $4k+3, k\ge 1$, there exist infinitely many contact manifolds that
are exactly fillable, almost Weinstein fillable but not Weinstein fillable. The
invariance of the structure maps generalizes to strong fillings with vanishing
first Chern class. We show that any strong filling with vanishing first Chern
class of a class of manifolds, including $(S^{2n-1},\xi_{std}), \partial(T^*L
\times \mathbb{C}^n)$ with $L$ simply connected, must be exact and have unique
diffeomorphism type. As an application of the proof, we show that the existence
of symplectic dilation implies uniruledness. In particular any affine exotic
$\mathbb{C}^n$ with non-negative log Kodaira dimension is a symplectic exotic
$\mathbb{C}^{n}$.
