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Squeezing in Floer theory
and refined Hofer–Zehnder capacities of sets near symplectic
submanifolds
Ely Kerman |
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Geometry & Topology 9 (2005) 1775–1834
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arXiv: math.SG/0502448 |
Abstract |
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We use Floer homology to study the Hofer–Zehnder capacity of neighborhoods near a closed symplectic submanifold of a geometrically bounded and symplectically aspherical ambient manifold. We prove that, when the unit normal bundle of is homologically trivial in degree (for example, if ), a refined version of the Hofer–Zehnder capacity is finite for all open sets close enough to . We compute this capacity for certain tubular neighborhoods of by using a squeezing argument in which the algebraic framework of Floer theory is used to detect nontrivial periodic orbits. As an application, we partially recover some existence results of Arnold for Hamiltonian flows which describe a charged particle moving in a nondegenerate magnetic field on a torus. Following an earlier paper, we also relate our refined capacity to the study of Hamiltonian paths with minimal Hofer length. |
Keywords
Hofer–Zehnder capacity, symplectic submanifold, Floer
homology
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Mathematical Subject Classification 2000
Primary: 53D40
Secondary: 37J45
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References |
Forward citations |
Publication
Received: 22 March 2005
Revised: 11 September 2005
Accepted: 12 August 2005
Published: 25 September 2005
Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, Eleny Ionel
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Authors |
| Ely Kerman | |
| Mathematics University of Illinois at Urbana–Champaign Urbana Illinois 61801 USA |
Institute of Science Walailak University Nakhon Si Thammarat 80160 Thailand |
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