Symplectic homology of disc cotangent bundles of domains in Euclidean space

Abstract

Let V be a bounded domain with smooth boundary in Rn, 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.