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

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.

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

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Citation Information
Yi Lin. "Symplectic Harmonic Theory and The Federer-Fleming Deformation Theorem" 2013
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