Space of symplectic forms
Tian-Jun Li and Ai-Ko Liu
(
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Let $M$ be a closed oriented smooth
$4-$manifold admitting symplectic structures. We study the number of
of equivalence classes of symplectic canonical classes on $M$.
If $M$ has $b^+=1$, we prove there
is a unique equivalence class. This
result, together with results of
Taubes and Witten, implies that the this number is finite for any $M$.
We also study which second cohomology class on $M$ is represented by symplectic forms. In particular, if $M$ is minimal and has $b^+=1$, we show that every class of positive square has symplectic representatives.
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