TY - JOUR

T1 - Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets near symplectic submanifolds

AU - Kerman, Ely

PY - 2005/9/25

Y1 - 2005/9/25

N2 - We use Floer homology to study the Hofer-Zehnder capacity of neighborhoods near a closed symplectic submanifold M of a geometrically bounded and symplectically aspherical ambient manifold. We prove that, when the unit normal bundle of M is homologically trivial in degree dim(M) (for example, if codim(M) > dim(M)), a refined version of the Hofer-Zehnder capacity is finite for all open sets close enough to M. We compute this capacity for certain tubular neighborhoods of M by using a squeezing argument in which the algebraic framework of Floer theory, is used to detect nontrivial periodic orbits [18, 19, 26]. We partially recover some existence results of Arnold [1] for Hamiltonian flows which describe a charged particle moving in a nondegenerate magnetic field on a torus. Following [43], we also relate our refined capacity to the study of Hamiltonian paths with minimal Hofer length.

AB - We use Floer homology to study the Hofer-Zehnder capacity of neighborhoods near a closed symplectic submanifold M of a geometrically bounded and symplectically aspherical ambient manifold. We prove that, when the unit normal bundle of M is homologically trivial in degree dim(M) (for example, if codim(M) > dim(M)), a refined version of the Hofer-Zehnder capacity is finite for all open sets close enough to M. We compute this capacity for certain tubular neighborhoods of M by using a squeezing argument in which the algebraic framework of Floer theory, is used to detect nontrivial periodic orbits [18, 19, 26]. We partially recover some existence results of Arnold [1] for Hamiltonian flows which describe a charged particle moving in a nondegenerate magnetic field on a torus. Following [43], we also relate our refined capacity to the study of Hamiltonian paths with minimal Hofer length.

KW - Floer homology

KW - Hofer-Zehnder capacity

KW - Symplectic submanifold

UR - http://www.scopus.com/inward/record.url?scp=25644431968&partnerID=8YFLogxK

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U2 - 10.2140/gt.2005.9.1775

DO - 10.2140/gt.2005.9.1775

M3 - Article

AN - SCOPUS:25644431968

SN - 1465-3060

VL - 9

SP - 1775

EP - 1834

JO - Geometry and Topology

JF - Geometry and Topology

ER -