2011/12/12 by Yi Lin, Lin, Yi · 1 citation
Mathematics · #53Dxx #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53Dxx
paper · pdf · doi:10.48550/arxiv.1112.2442
Some minor mistakes in the verion 2 are corrected
openalex publication_date 2011/12/12 · arxiv created 2013/09/29 · arxiv updated 2013/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.