Symplectic homology of disc cotangent bundles of domains in Euclidean space

2012/11/09 by Kei Irie, Irie, Kei · 1 citation
Mathematics · #53D40 #70H12 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1211.2184

openalex publication_date 2012/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Cited by

• Periodic billiard trajectories and Morse theory on loop spaces

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