Hodge Structure on Symplectic Manifolds
Copyright policy )Hodge Structure on Symplectic Manifolds
The article deals with symplectic harmonic forms. A recent result by O. Mathieu states: For a symplectic manifold of \(\dim 2n\) the following properties are equivalent: (1) There exists a harmonic cocycle in every cohomology class and (2) the cup product is surjective. This article provides an alternative, more direct proof for this fact using a particular \(\text{sl}(2,C)\) representation. An application in symplectic differential topology concludes the paper.
- Stony Brook University United States
- Institute of Mathematical Sciences Spain
Mathematics(all), General geometric structures on manifolds (almost complex, almost product structures, etc.), symplectic harmonic forms, Algebraic topology on manifolds and differential topology, Hodge theory in global analysis, symplectic de Rham theory, de Rham cohomology and algebraic geometry
Mathematics(all), General geometric structures on manifolds (almost complex, almost product structures, etc.), symplectic harmonic forms, Algebraic topology on manifolds and differential topology, Hodge theory in global analysis, symplectic de Rham theory, de Rham cohomology and algebraic geometry
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).61 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!