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Symplectic Harmonic Theory and The Federer-Fleming Deformation Theorem
(2013)
  • Yi Lin, Georgia Southern University
Abstract

In this article, we initiate a geometric measure theoretic approach to symplectic Hodge theory. In particular, we apply one of the central results in geometric measure theory, the Federer-Fleming deformation theorem, together with the cohomology theory of normal cur- rents on a differential manifold, to establish a fundamental property on symplectic Harmonic forms. We show that on a closed symplectic manifold, every real primitive cohomology class of positive degrees admits a symplectic Harmonic representative not supported on the entire mani- fold. As an application, we use it to investigate the support of symplectic Harmonic representatives of Thom classes, and give a complete solution to an open question asked by Guillemin.

Keywords
  • Symplectic Hodge theory,
  • Federer-Fleming deformation theorem
Disciplines
Publication Date
January 1, 2013
Comments

This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the author must have permission to distribute the work or the work must be available under the Creative Commons Attribution license, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration.

Citation Information
Yi Lin. "Symplectic Harmonic Theory and The Federer-Fleming Deformation Theorem" 2013
source:http://arxiv.org/abs/1112.2442v3
Available at: http://works.bepress.com/yi_lin/8