Symplectic homology of disc cotangent bundles of domains in Euclidean space

Abstract

Let $V$ be a bounded domain with smooth boundary in $\mathbb{R}^n$, and $D^*V$ denote its disc cotangent bundle. We compute symplectic homology of $D^*V$, in terms of relative homology of loop spaces on the closure of $V$. We use this result to show that the Floer-Hofer-Wysocki capacity of $D^*V$ is between $2r(V)$ and $2(n + 1)r(V)$, where $r(V)$ denotes the inradius of $V$. As an application, we study periodic billiard trajectories on $V$.