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

Mathematics – Symplectic Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper40.abs.html

Scientific paper

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. 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. We also relate our refined capacity to the study of Hamiltonian paths with minimal Hofer length.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets near symplectic submanifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets near symplectic submanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets near symplectic submanifolds will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-472107

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.