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arXiv · 1211.2184

Symplectic homology of disc cotangent bundles of domains in Euclidean space

Kei Irie
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Abstract

Let $V$ be a bounded domain with smooth boundary in $\R^n$, 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 Floer-Hofer capacity of $D^*V$ is between $2r(V)$ and $2(n+1)r(V)$, where $r(V)$ denotes inradius of $V$. As an application, we study periodic billiard trajectories on $V$.

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Kei Irie. 2013-06-17. Symplectic homology of disc cotangent bundles of domains in Euclidean space. https://arxiv.org/abs/1211.2184

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