Symplectic fillings of asymptotically dynamically convex manifolds II–k-dilations

We introduce the concept of $k$-(semi)-dilation for Liouville domains, which is a generalization symplectic dilation defined by Seidel-Solomon. prove that existence property independent fillings asymptotically dynamically convex (ADC) manifolds. construct examples with $k$-dilations, but not $k-1$-dilations all $k\ge 0$. extract invariants taking value in $\mathbb{N} \cup \{\infty\}$ domains and ADC contact manifolds, are called order (semi)-dilation. The (semi)-dilation serves as embedding cobordism obstructions. determine many Brieskorn varieties use them to study cobordisms between