5 problems

Let $(W,\omega)$ be a Liouville domain, and let ${\rm SH}^*(W,\omega)$ denote its symplectic homology. Equip $\operatorname{Ham}(W,\omega)$ with the metric $d_{\gamma}$. Infinite q…

Let $Y$ be a compact manifold without boundary, let $M\subset J^1Y$ be a closed tubular neighborhood of the zero-section, and let $\Lambda\subset(M,\ker(dz-pdq))$ be a Legendrian s…

Let $M^{in} \subset M$ be an inclusion of Liouville subdomains, and let $\EuScript{W}(M)$ denote the wrapped Fukaya category of $M$, with $\operatorname{Tw}(\EuScript{W}(M^{in}))$…

Let $W$ be a Liouville domain of dimension $4n+2$. A Liouville domain $W^{\prime}$ is required to be diffeomorphic to $W$ and to have vanishing symplectic homology and wrapped Fuka…

The constructions give pairs of Liouville domains that are diffeomorphic but have different symplectic invariants, including examples with vanishing wrapped Fukaya categories. Dopp…